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  1. <html><head><meta charset="UTF-8"><meta name="viewport" content="width=device-width,initial-scale=1"><title>Cerebry Teacher Dashboard</title><link rel="shortcut icon" href="assets/favicon.ico" type="image/x-icon"><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.9.0/katex.min.css"><style>@font-face {
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href="blob:https://teacherdashboard.cerebry.co/7588f1f2-1aa3-4ba2-bf8f-d4dd45dd2570"><link type="text/css" rel="stylesheet" href="blob:https://teacherdashboard.cerebry.co/75ce9a6c-1b84-4aee-af60-dd820e233215"><link type="text/css" rel="stylesheet" href="blob:https://teacherdashboard.cerebry.co/36fb6306-d7a1-4cb0-87a9-a56dbf207e0e"><link type="text/css" rel="stylesheet" href="blob:https://teacherdashboard.cerebry.co/ac18c324-27e3-49a8-99a7-913ae8ac1beb"><link type="text/css" rel="stylesheet" href="blob:https://teacherdashboard.cerebry.co/b11afc83-abdb-4483-92fc-b650ec330903"><link type="text/css" rel="stylesheet" href="blob:https://teacherdashboard.cerebry.co/5b13b81b-960e-4bfd-b24a-2688c90b9e2e"><link type="text/css" rel="stylesheet" href="blob:https://teacherdashboard.cerebry.co/59797ec7-4a25-4ad3-bc40-98d3f6ecbb18"></head><body><div id="app" class="container"><div class="teacher-dashboard" cerebry-widget-host="teacher-dashboard"><div class="dashboard-container__1bwpr"><div class="syllabus-container__16p5n"><div class="header-section__3qj4i"><div class="logo__25ZGV"><img src="./../../assets/images/logo.svg"></div><div class="topic-header-container__1aQvM"><div class="topic-header__35qsF"><div class="topic-name__36YxS">Lines, angels and shapes</div></div></div></div><div class="syllabus-section__1RMDs"><div class="syllabus-list__tJnEc"><div class="syllabus-heading__2owpJ selected-exercise__mQhSL"><div class="exercise-name__35uEj">Exercise 3.1</div><div class="arrow-container__1VE8J display-arrow__3FPW_"><svg version="1.2" overflow="visible" preserveAspectRatio="none" viewBox="0 0 24 24" width="20" height="20"><g><path d="M7 10l5 5 5-5z" vector-effect="non-scaling-stroke" style="fill: rgb(255, 255, 255);"></path></g></svg></div></div><div class="syllabus-heading__2owpJ "><div class="exercise-name__35uEj">Exercise 3.2</div><div class="arrow-container__1VE8J "><svg version="1.2" overflow="visible" preserveAspectRatio="none" viewBox="0 0 24 24" width="20" height="20"><g><path d="M7 10l5 5 5-5z" vector-effect="non-scaling-stroke" style="fill: rgb(255, 255, 255);"></path></g></svg></div></div><div class="syllabus-heading__2owpJ "><div class="exercise-name__35uEj">Exercise 3.3</div><div class="arrow-container__1VE8J "><svg version="1.2" overflow="visible" preserveAspectRatio="none" viewBox="0 0 24 24" width="20" height="20"><g><path d="M7 10l5 5 5-5z" vector-effect="non-scaling-stroke" style="fill: rgb(255, 255, 255);"></path></g></svg></div></div><div class="syllabus-heading__2owpJ "><div class="exercise-name__35uEj">Exercise 3.4</div><div class="arrow-container__1VE8J "><svg version="1.2" overflow="visible" preserveAspectRatio="none" viewBox="0 0 24 24" width="20" height="20"><g><path d="M7 10l5 5 5-5z" vector-effect="non-scaling-stroke" style="fill: rgb(255, 255, 255);"></path></g></svg></div></div></div><div class="syllabus-content__3CLeY"><div class="subtopic-name__2muyf">3.1 Lines And Angles</div><div class="subtopic-level__1Gg9u"><div class="level-name__xXnll level-selected__13Sd1">Easy</div><div class="level-name__xXnll ">Medium</div><div class="level-name__xXnll ">Hard</div></div><div class="questions-wrapper__OmCJ6"><div><div class="question-info-container__1jee9"><div class="question-heading-section__1U6d5"><div class="question-number__SpJ1d">Question 1</div><div class="content-button__3Q0iO">Show Content</div></div><div class="question-container__N3ddu"><div class="question-display-info__2bd0J"><div class="question-content__3NN6L"><div><div>
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  49.             <div><div class="_33s8iDB86ShboS4mZ56Q4l"><div class="solution"><div id="figure-box-0" class="_1gd72wi83IbxAsemSie8HX" style="user-select: none; overflow: hidden; position: relative; touch-action: none;"><svg width="400" height="400" style="overflow: hidden; width: 400px; height: 400px;"><defs><filter id="figure-box-0_f1" width="300%" height="300%" filterUnits="userSpaceOnUse"><feOffset result="offOut" in="SourceAlpha" dx="5" dy="5"></feOffset><feGaussianBlur result="blurOut" in="offOut" stdDeviation="3"></feGaussianBlur><feBlend in="SourceGraphic" in2="blurOut" mode="normal"></feBlend></filter><marker id="figure-box-0_jxgBoard1L5TriangleStart" stroke="#333" stroke-opacity="1" fill="#333" fill-opacity="1" stroke-width="0" orient="auto" markerUnits="strokeWidth" refY="5" refX="0.1" viewBox="0 0 80 80" markerHeight="64" markerWidth="64" display="inherit" style="position: absolute;"><path d="M 0,0 L 10,5 L 0,10 z"></path></marker><marker id="figure-box-0_jxgBoard1L8TriangleStart" stroke="#333" stroke-opacity="1" fill="#333" fill-opacity="1" stroke-width="0" orient="auto" markerUnits="strokeWidth" refY="5" refX="0.1" viewBox="0 0 80 80" markerHeight="64" markerWidth="64" display="inherit" style="position: absolute;"><path d="M 0,0 L 10,5 L 0,10 z"></path></marker><marker id="figure-box-0_jxgBoard1L11TriangleStart" stroke="#333" stroke-opacity="1" fill="#333" fill-opacity="1" stroke-width="0" orient="auto" markerUnits="strokeWidth" refY="5" refX="0.1" viewBox="0 0 80 80" markerHeight="64" markerWidth="64" display="inherit" style="position: absolute;"><path d="M 0,0 L 10,5 L 0,10 z"></path></marker><marker id="figure-box-0_jxgBoard1L14TriangleStart" stroke="#333" stroke-opacity="1" fill="#333" fill-opacity="1" stroke-width="0" orient="auto" markerUnits="strokeWidth" refY="5" refX="0.1" viewBox="0 0 80 80" markerHeight="64" markerWidth="64" display="inherit" style="position: absolute;"><path d="M 0,0 L 10,5 L 0,10 z"></path></marker></defs><g></g><g></g><g></g><g><path id="figure-box-0_jxgBoard1G16" stroke-linecap="round" stroke-linejoin="round" stroke="#333" stroke-opacity="1" stroke-width="1px" fill="#fff" fill-opacity="0.3" d=" M 120.36361039487487 195.42373251639188 L 119.25380791732927 215.39291723837874 L 139.22299263931612 216.50271971592434 L 140.33279511686175 196.53353499393748 L 120.36361039487487 195.42373251639188" display="inline" style="position: absolute; transition: fill 100ms ease 0s, fill-opacity 100ms ease 0s, stroke 100ms ease 0s, stroke-opacity 100ms ease 0s; visibility: inherit;"></path></g><g></g><g></g><g></g><g><line id="figure-box-0_jxgBoard1L5" stroke="#333" stroke-opacity="1" stroke-width="1px" fill="#333" fill-opacity="1" x1="120" y1="195" x2="111.4254326590894" y2="356.01132006821024" marker-end="url(#figure-box-0_jxgBoard1L5TriangleStart)" stroke-linecap="butt" display="inline" style="position: absolute; transition: fill 100ms ease 0s, fill-opacity 100ms ease 0s, stroke 100ms ease 0s, stroke-opacity 100ms ease 0s; visibility: inherit;"></line><line id="figure-box-0_jxgBoard1L8" stroke="#333" stroke-opacity="1" stroke-width="1px" fill="#333" fill-opacity="1" x1="120" y1="195" x2="281.0139684420009" y2="204.52745375396455" marker-end="url(#figure-box-0_jxgBoard1L8TriangleStart)" stroke-linecap="butt" display="inline" style="position: absolute; transition: fill 100ms ease 0s, fill-opacity 100ms ease 0s, stroke 100ms ease 0s, stroke-opacity 100ms ease 0s; 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transition: fill 100ms ease 0s, fill-opacity 100ms ease 0s, stroke 100ms ease 0s, stroke-opacity 100ms ease 0s; visibility: inherit;" display="inline"></path><path id="figure-box-0_jxgBoard1P9" stroke-linecap="round" stroke-linejoin="round" stroke="#333" stroke-opacity="1" stroke-width="2px" fill="#333" fill-opacity="1" d="M 0 0" style="position: absolute; transition: fill 100ms ease 0s, fill-opacity 100ms ease 0s, stroke 100ms ease 0s, stroke-opacity 100ms ease 0s; visibility: inherit;" display="inline"></path><path id="figure-box-0_jxgBoard1P12" stroke-linecap="round" stroke-linejoin="round" stroke="#333" stroke-opacity="1" stroke-width="2px" fill="#333" fill-opacity="1" d="M 0 0" style="position: absolute; transition: fill 100ms ease 0s, fill-opacity 100ms ease 0s, stroke 100ms ease 0s, stroke-opacity 100ms ease 0s; visibility: inherit;" display="inline"></path><path id="figure-box-0_jxgBoard1P15" stroke-linecap="round" stroke-linejoin="round" stroke="#333" stroke-opacity="1" stroke-width="1px" fill="#333" fill-opacity="1" d="M 0 0" display="inline" style="position: absolute; transition: fill 100ms ease 0s, fill-opacity 100ms ease 0s, stroke 100ms ease 0s, stroke-opacity 100ms ease 0s; visibility: inherit;"></path><ellipse id="figure-box-0_jxgBoard1P18" stroke="none" stroke-opacity="1" stroke-width="2px" fill="black" fill-opacity="1" cx="120" cy="195" rx="3" ry="3" display="none" style="position: absolute; transition: fill 100ms ease 0s, fill-opacity 100ms ease 0s, stroke 100ms ease 0s, stroke-opacity 100ms ease 0s; visibility: hidden;"></ellipse></g><g></g><g></g><g></g><g></g><g></g><g></g><g></g><g></g><g></g><g></g><foreignObject x="0" y="0" width="100%" height="100%" id="figure-box-0_foreignObj"></foreignObject></svg><div class="JXGinfobox" id="figure-box-0_jxgBoard1_infobox" display="none" style="position: absolute; z-index: 9; font-family: Arial, Helvetica, Geneva, sans-serif; font-size: 12px; color: rgb(187, 187, 187); opacity: 1; left: 120px; right: auto; bottom: auto; top: 194px; visibility: hidden;">0,0</div><div id="figure-box-0_navigationbar" class="JXG_navigation" style="color: rgb(51, 51, 51); background-color: transparent; padding: 2px; position: absolute; font-size: 14px; cursor: pointer; z-index: 100; right: 5px; bottom: 5px;"></div><div class="JXGtext" id="figure-box-0_jxgBoard1P1Label" display="inline" style="position: absolute; z-index: 9; font-family: Arial, Helvetica, Geneva, sans-serif; font-size: 12px; transition: color 100ms ease 0s, opacity 100ms ease 0s; color: black; opacity: 1; left: 99px; right: auto; bottom: auto; top: 190px; visibility: inherit;">B</div><div class="JXGtext" id="figure-box-0_jxgBoard1P3Label" display="inline" style="position: absolute; z-index: 9; font-family: Arial, Helvetica, Geneva, sans-serif; font-size: 12px; transition: color 100ms ease 0s, opacity 100ms ease 0s; color: black; opacity: 1; left: 106px; right: auto; bottom: auto; top: 373px; visibility: inherit;">Z</div><div class="JXGtext" id="figure-box-0_jxgBoard1P6Label" display="inline" style="position: absolute; z-index: 9; font-family: Arial, Helvetica, Geneva, sans-serif; font-size: 12px; transition: color 100ms ease 0s, opacity 100ms ease 0s; color: black; opacity: 1; left: 302px; right: auto; bottom: auto; top: 198px; visibility: inherit;">P</div><div class="JXGtext" id="figure-box-0_jxgBoard1P9Label" display="inline" style="position: absolute; z-index: 9; font-family: Arial, Helvetica, Geneva, sans-serif; font-size: 12px; transition: color 100ms ease 0s, opacity 100ms ease 0s; color: black; opacity: 1; left: 281px; right: auto; bottom: auto; top: 102px; visibility: inherit;">J</div><div class="JXGtext" id="figure-box-0_jxgBoard1P12Label" display="inline" style="position: absolute; z-index: 9; font-family: Arial, Helvetica, Geneva, sans-serif; font-size: 12px; transition: color 100ms ease 0s, opacity 100ms ease 0s; color: black; opacity: 1; left: 178px; right: auto; bottom: auto; top: 12px; visibility: inherit;">S</div></div><p class="kLnDsmZC8c49r2Ntz8LHD"><span>State whether following statement is true or false in context of the given figure, &nbsp;</span><span><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">∠</mi><mrow><mi>Z</mi><mi>B</mi><mi>P</mi></mrow></mrow><annotation encoding="application/x-tex">\angle{ZBP}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.69224em;"></span><span class="strut bottom" style="height:0.69224em;vertical-align:0em;"></span><span class="base"><span class="mord">∠</span><span class="mord"><span class="mord mathit" style="margin-right:0.07153em;">Z</span><span class="mord mathit" style="margin-right:0.05017em;">B</span><span class="mord mathit" style="margin-right:0.13889em;">P</span></span></span></span></span></span><span>&nbsp;</span><span> is Right angle. </span></p></div><div></div></div></div>
  50.         </div></div></div><div class="horizontal-line__36CRY"></div><div class="solution-content__1ldKV"><div><div>
  51.             <style type="text/css">.kLnDsmZC8c49r2Ntz8LHD{display:table}._33s8iDB86ShboS4mZ56Q4l{width:100%}@media screen and (max-width:768px){.kLnDsmZC8c49r2Ntz8LHD{font-size:14px}}</style>
  52.             <div><div class="_33s8iDB86ShboS4mZ56Q4l"><div class="solution"><div></div><p class="kLnDsmZC8c49r2Ntz8LHD"><span>Angles whose measure is  90</span><span><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">°</mi></mrow><annotation encoding="application/x-tex">\degree</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.69444em;"></span><span class="strut bottom" style="height:0.69444em;vertical-align:0em;"></span><span class="base"><span class="mord">°</span></span></span></span></span><span>are right angles.</span></p><p class="kLnDsmZC8c49r2Ntz8LHD"><span>So true, from figure &nbsp;</span><span><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">∠</mi><mrow><mi>Z</mi><mi>B</mi><mi>P</mi></mrow></mrow><annotation encoding="application/x-tex">\angle{ZBP}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.69224em;"></span><span class="strut bottom" style="height:0.69224em;vertical-align:0em;"></span><span class="base"><span class="mord">∠</span><span class="mord"><span class="mord mathit" style="margin-right:0.07153em;">Z</span><span class="mord mathit" style="margin-right:0.05017em;">B</span><span class="mord mathit" style="margin-right:0.13889em;">P</span></span></span></span></span></span><span>&nbsp;</span><span> is Right angle.</span></p></div><div></div></div></div>
  53.         </div></div></div></div></div></div></div><div><div class="question-info-container__1jee9"><div class="question-heading-section__1U6d5"><div class="question-number__SpJ1d">Question 2</div><div class="content-button__3Q0iO">Show Content</div></div><div class="question-container__N3ddu"><div class="question-display-info__2bd0J"><div class="question-content__3NN6L"><div><div>
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  55.             <div><div class="_33s8iDB86ShboS4mZ56Q4l"><div class="solution"><div class="_1jh53Fsi5ZX-jFVRit_PGA">                     <div id="figure-box-0" class="_1gd72wi83IbxAsemSie8HX" style="user-select: none; overflow: hidden; position: relative; touch-action: none;"><svg width="400" height="400" style="overflow: hidden; width: 400px; height: 400px;"><defs><filter id="figure-box-0_f1" width="300%" height="300%" filterUnits="userSpaceOnUse"><feOffset result="offOut" in="SourceAlpha" dx="5" dy="5"></feOffset><feGaussianBlur result="blurOut" in="offOut" stdDeviation="3"></feGaussianBlur><feBlend in="SourceGraphic" in2="blurOut" mode="normal"></feBlend></filter></defs><g></g><g></g><g></g><g></g><g></g><g></g><g></g><g><line id="figure-box-0_jxgBoard1L9" stroke="#333" stroke-opacity="1" stroke-width="1px" fill="#333" fill-opacity="1" x1="328" y1="360" x2="72" y2="151" stroke-linecap="butt" display="inline" style="position: absolute; transition: fill 100ms ease 0s, fill-opacity 100ms ease 0s, stroke 100ms ease 0s, stroke-opacity 100ms ease 0s; visibility: inherit;"></line><line id="figure-box-0_jxgBoard1L10" stroke="#333" stroke-opacity="1" stroke-width="1px" fill="#333" fill-opacity="1" x1="328" y1="360" x2="243" y2="40" stroke-linecap="butt" display="inline" style="position: absolute; transition: fill 100ms ease 0s, fill-opacity 100ms ease 0s, stroke 100ms ease 0s, stroke-opacity 100ms ease 0s; visibility: inherit;"></line></g><g></g><g><ellipse id="figure-box-0_jxgBoard1P1" stroke="#333" stroke-opacity="1" stroke-width="1px" fill="#333" fill-opacity="1" cx="72" cy="151" rx="3" ry="3" style="position: absolute; transition: fill 100ms ease 0s, fill-opacity 100ms ease 0s, stroke 100ms ease 0s, stroke-opacity 100ms ease 0s; visibility: inherit;" display="inline"></ellipse><ellipse id="figure-box-0_jxgBoard1P3" stroke="#333" stroke-opacity="1" stroke-width="1px" fill="#333" fill-opacity="1" cx="256" cy="211" rx="3" ry="3" style="position: absolute; transition: fill 100ms ease 0s, fill-opacity 100ms ease 0s, stroke 100ms ease 0s, stroke-opacity 100ms ease 0s; visibility: inherit;" display="inline"></ellipse><ellipse id="figure-box-0_jxgBoard1P5" stroke="#333" stroke-opacity="1" stroke-width="1px" fill="#333" fill-opacity="1" cx="243" cy="40" rx="3" ry="3" style="position: absolute; transition: fill 100ms ease 0s, fill-opacity 100ms ease 0s, stroke 100ms ease 0s, stroke-opacity 100ms ease 0s; visibility: inherit;" display="inline"></ellipse><ellipse id="figure-box-0_jxgBoard1P7" stroke="#333" stroke-opacity="1" stroke-width="1px" fill="#333" fill-opacity="1" cx="328" cy="360" rx="3" ry="3" style="position: absolute; transition: fill 100ms ease 0s, fill-opacity 100ms ease 0s, stroke 100ms ease 0s, stroke-opacity 100ms ease 0s; visibility: inherit;" display="inline"></ellipse></g><g></g><g></g><g></g><g></g><g></g><g></g><g></g><g></g><g></g><g></g><foreignObject x="0" y="0" width="100%" height="100%" id="figure-box-0_foreignObj"></foreignObject></svg><div class="JXGinfobox" id="figure-box-0_jxgBoard1_infobox" display="none" style="position: absolute; z-index: 9; font-family: Arial, Helvetica, Geneva, sans-serif; font-size: 12px; color: rgb(187, 187, 187); opacity: 1; left: 328px; right: auto; bottom: auto; top: 359px; visibility: hidden;">0,0</div><div id="figure-box-0_navigationbar" class="JXG_navigation" style="color: rgb(51, 51, 51); background-color: transparent; padding: 2px; position: absolute; font-size: 14px; cursor: pointer; z-index: 100; right: 5px; bottom: 5px;"></div><div class="JXGtext" id="figure-box-0_jxgBoard1P1Label" display="inline" style="position: absolute; z-index: 9; font-family: Arial, Helvetica, Geneva, sans-serif; font-size: 12px; transition: color 100ms ease 0s, opacity 100ms ease 0s; color: black; opacity: 1; left: 55px; right: auto; bottom: auto; top: 133px; visibility: inherit;">J</div><div class="JXGtext" id="figure-box-0_jxgBoard1P3Label" display="inline" style="position: absolute; z-index: 9; font-family: Arial, Helvetica, Geneva, sans-serif; font-size: 12px; transition: color 100ms ease 0s, opacity 100ms ease 0s; color: black; opacity: 1; left: 254px; right: auto; bottom: auto; top: 187px; visibility: inherit;">H</div><div class="JXGtext" id="figure-box-0_jxgBoard1P5Label" display="inline" style="position: absolute; z-index: 9; font-family: Arial, Helvetica, Geneva, sans-serif; font-size: 12px; transition: color 100ms ease 0s, opacity 100ms ease 0s; color: black; opacity: 1; left: 235px; right: auto; bottom: auto; top: 16px; visibility: inherit;">D</div><div class="JXGtext" id="figure-box-0_jxgBoard1P7Label" display="inline" style="position: absolute; z-index: 9; font-family: Arial, Helvetica, Geneva, sans-serif; font-size: 12px; transition: color 100ms ease 0s, opacity 100ms ease 0s; color: black; opacity: 1; left: 333px; right: auto; bottom: auto; top: 367px; visibility: inherit;">F</div></div></div><p class="kLnDsmZC8c49r2Ntz8LHD"><span> From the figure, identify the interior point of &nbsp;</span><span><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">∠</mi></mrow><annotation encoding="application/x-tex">\angle</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.69224em;"></span><span class="strut bottom" style="height:0.69224em;vertical-align:0em;"></span><span class="base"><span class="mord">∠</span></span></span></span></span><span>JFD. </span></p></div><div></div></div></div>
  56.         </div></div></div><div class="horizontal-line__36CRY"></div><div class="solution-content__1ldKV"><div><div>
  57.             <style type="text/css">.kLnDsmZC8c49r2Ntz8LHD{display:table}._33s8iDB86ShboS4mZ56Q4l{width:100%}@media screen and (max-width:768px){.kLnDsmZC8c49r2Ntz8LHD{font-size:14px}}</style>
  58.             <div><div class="_33s8iDB86ShboS4mZ56Q4l"><div class="solution"><div></div><p class="kLnDsmZC8c49r2Ntz8LHD"><span>Interior point of the angle is generally the point which lies between the line forming an acute angle but is not touching them. Hence H is the interior point of &nbsp;</span><span><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">∠</mi></mrow><annotation encoding="application/x-tex">\angle</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.69224em;"></span><span class="strut bottom" style="height:0.69224em;vertical-align:0em;"></span><span class="base"><span class="mord">∠</span></span></span></span></span><span>JFD.</span></p></div><div></div></div></div>
  59.         </div></div></div></div></div></div></div><div><div class="question-info-container__1jee9"><div class="question-heading-section__1U6d5"><div class="question-number__SpJ1d">Question 3</div><div class="content-button__3Q0iO">Show Content</div></div><div class="question-container__N3ddu"><div class="question-display-info__2bd0J"><div class="question-content__3NN6L"><div><div>
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  61.             <div><div class="_33s8iDB86ShboS4mZ56Q4l"><div class="solution"><div id="figure-box-0" class="_1gd72wi83IbxAsemSie8HX" style="user-select: none; overflow: hidden; position: relative; touch-action: none;"><svg width="400" height="400" style="overflow: hidden; width: 400px; height: 400px;"><defs><filter id="figure-box-0_f1" width="300%" height="300%" filterUnits="userSpaceOnUse"><feOffset result="offOut" in="SourceAlpha" dx="5" dy="5"></feOffset><feGaussianBlur result="blurOut" in="offOut" stdDeviation="3"></feGaussianBlur><feBlend in="SourceGraphic" in2="blurOut" mode="normal"></feBlend></filter><marker id="figure-box-0_jxgBoard1L5TriangleStart" stroke="#333" stroke-opacity="1" fill="#333" fill-opacity="1" stroke-width="0" orient="auto" markerUnits="strokeWidth" refY="5" refX="0.1" viewBox="0 0 80 80" markerHeight="64" markerWidth="64" display="inherit" style="position: absolute;"><path d="M 0,0 L 10,5 L 0,10 z"></path></marker><marker id="figure-box-0_jxgBoard1L8TriangleEnd" stroke="#333" stroke-opacity="1" fill="#333" fill-opacity="1" stroke-width="0" orient="auto" markerUnits="strokeWidth" refY="5" refX="9.9" viewBox="0 0 80 80" markerHeight="64" markerWidth="64" display="inherit" style="position: absolute;"><path d="M 10,0 L 0,5 L 10,10 z"></path></marker></defs><g></g><g></g><g></g><g><path id="figure-box-0_jxgBoard1G9" stroke-linecap="round" stroke-linejoin="round" stroke="#333" stroke-opacity="1" stroke-width="1px" fill="#fff" fill-opacity="0.3" d=" M 317.7874751712349 36.065573770491824 C 311.32741136500226 42.3190253469736 304.8673475587696 48.57247692345538 298.3878841615272 54.84470763380051 C 303.46906065341926 60.09376472601508 310.46043391455174 63.05974761082166 317.7659743500451 63.06556520965137 C 317.77313412350134 54.07456806041125 317.7802938969575 45.08357091117108 317.7874751712349 36.065573770491824" display="inline" style="position: absolute; transition: fill 100ms ease 0s, fill-opacity 100ms ease 0s, stroke 100ms ease 0s, stroke-opacity 100ms ease 0s; visibility: inherit;"></path></g><g></g><g></g><g></g><g><line id="figure-box-0_jxgBoard1L5" stroke="#333" stroke-opacity="1" stroke-width="1px" fill="#333" fill-opacity="1" x1="318" y1="36" x2="318" y2="356" marker-end="url(#figure-box-0_jxgBoard1L5TriangleStart)" stroke-linecap="butt" display="inline" style="position: absolute; transition: fill 100ms ease 0s, fill-opacity 100ms ease 0s, stroke 100ms ease 0s, stroke-opacity 100ms ease 0s; visibility: inherit;"></line><line id="figure-box-0_jxgBoard1L8" stroke="#333" stroke-opacity="1" stroke-width="1px" fill="#333" fill-opacity="1" x1="87.75353112067818" y1="258.44150383256516" x2="318" y2="36" marker-start="url(#figure-box-0_jxgBoard1L8TriangleEnd)" stroke-linecap="butt" display="inline" style="position: absolute; transition: fill 100ms ease 0s, fill-opacity 100ms ease 0s, stroke 100ms ease 0s, stroke-opacity 100ms ease 0s; 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z-index: 9; font-family: Arial, Helvetica, Geneva, sans-serif; font-size: 12px; color: rgb(187, 187, 187); opacity: 1; left: 318px; right: auto; bottom: auto; top: 363px; visibility: hidden;">0,0</div><div id="figure-box-0_navigationbar" class="JXG_navigation" style="color: rgb(51, 51, 51); background-color: transparent; padding: 2px; position: absolute; font-size: 14px; cursor: pointer; z-index: 100; right: 5px; bottom: 5px;"></div><div class="JXGtext" id="figure-box-0_jxgBoard1P1Label" display="inline" style="position: absolute; z-index: 9; font-family: Arial, Helvetica, Geneva, sans-serif; font-size: 12px; transition: color 100ms ease 0s, opacity 100ms ease 0s; color: black; opacity: 1; left: 321px; right: auto; bottom: auto; top: 13px; visibility: inherit;">P</div><div class="JXGtext" id="figure-box-0_jxgBoard1P3Label" display="inline" style="position: absolute; z-index: 9; font-family: Arial, Helvetica, Geneva, sans-serif; font-size: 12px; transition: color 100ms ease 0s, opacity 100ms ease 0s; color: black; opacity: 1; left: 314px; right: auto; bottom: auto; top: 373px; visibility: inherit;">R</div><div class="JXGtext" id="figure-box-0_jxgBoard1P6Label" display="inline" style="position: absolute; z-index: 9; font-family: Arial, Helvetica, Geneva, sans-serif; font-size: 12px; transition: color 100ms ease 0s, opacity 100ms ease 0s; color: black; opacity: 1; left: 66px; right: auto; bottom: auto; top: 268px; visibility: inherit;">F</div><div class="JXGtext" id="figure-box-0_jxgBoard1T12" display="inline" style="position: absolute; z-index: 9; font-family: Arial, Helvetica, Geneva, sans-serif; font-size: 12px; transition: color 100ms ease 0s, opacity 100ms ease 0s; color: black; opacity: 1; left: 280px; right: auto; bottom: auto; top: 101px; visibility: inherit;">46°</div></div><p class="kLnDsmZC8c49r2Ntz8LHD"><span>Find out whether &nbsp;</span><span><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">∠</mi></mrow><annotation encoding="application/x-tex">\angle</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.69224em;"></span><span class="strut bottom" style="height:0.69224em;vertical-align:0em;"></span><span class="base"><span class="mord">∠</span></span></span></span></span><span>RPF is a right, acute or obtuse angle. </span></p></div><div></div></div></div>
  62.         </div></div></div><div class="horizontal-line__36CRY"></div><div class="solution-content__1ldKV"><div><div>
  63.             <style type="text/css">.kLnDsmZC8c49r2Ntz8LHD{display:table}._33s8iDB86ShboS4mZ56Q4l{width:100%}@media screen and (max-width:768px){.kLnDsmZC8c49r2Ntz8LHD{font-size:14px}}</style>
  64.             <div><div class="_33s8iDB86ShboS4mZ56Q4l"><div class="solution"><div></div><p class="kLnDsmZC8c49r2Ntz8LHD"><span>Acute angle is less than 90</span><span><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">°</mi></mrow><annotation encoding="application/x-tex">\degree</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.69444em;"></span><span class="strut bottom" style="height:0.69444em;vertical-align:0em;"></span><span class="base"><span class="mord">°</span></span></span></span></span><span>. Hence, from the figure &nbsp;</span><span><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">∠</mi></mrow><annotation encoding="application/x-tex">\angle</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.69224em;"></span><span class="strut bottom" style="height:0.69224em;vertical-align:0em;"></span><span class="base"><span class="mord">∠</span></span></span></span></span><span>RPF is acute angle.</span></p></div><div></div></div></div>
  65.         </div></div></div></div></div></div></div><div><div class="question-info-container__1jee9"><div class="question-heading-section__1U6d5"><div class="question-number__SpJ1d">Question 4</div><div class="content-button__3Q0iO">Show Content</div></div><div class="question-container__N3ddu"><div class="question-display-info__2bd0J"><div class="question-content__3NN6L"><div><div>
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  67.             <div><div class="_33s8iDB86ShboS4mZ56Q4l"><div class="solution"><div id="figure-box-0" class="_1gd72wi83IbxAsemSie8HX" style="user-select: none; overflow: hidden; position: relative; touch-action: none;"><svg width="400" height="400" style="overflow: hidden; width: 400px; height: 400px;"><defs><filter id="figure-box-0_f1" width="300%" height="300%" filterUnits="userSpaceOnUse"><feOffset result="offOut" in="SourceAlpha" dx="5" dy="5"></feOffset><feGaussianBlur result="blurOut" in="offOut" stdDeviation="3"></feGaussianBlur><feBlend in="SourceGraphic" in2="blurOut" mode="normal"></feBlend></filter></defs><g></g><g></g><g></g><g><path id="figure-box-0_jxgBoard1G15" stroke-linecap="round" stroke-linejoin="round" stroke="#333" stroke-opacity="1" stroke-width="1px" fill="#fff" fill-opacity="0.3" d=" M 200.00000000000003 274.28752352759426 C 205.7883841643954 264.6540345268284 211.5767683287908 255.02054552606253 217.38253502821436 245.35812712889796 C 207.76532352482016 239.57952347164957 195.9051896388896 238.9579601926884 185.73663366625144 243.69963571510732 C 190.4863346553897 253.88540235666548 195.236035644528 264.07116899822364 200.00000000000003 274.28752352759426" display="inline" style="position: absolute; 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font-size: 12px; transition: color 100ms ease 0s, opacity 100ms ease 0s; color: black; opacity: 1; left: 377px; right: auto; bottom: auto; top: 267px; visibility: inherit;">X</div><div class="JXGtext" id="figure-box-0_jxgBoard1P3Label" display="inline" style="position: absolute; z-index: 9; font-family: Arial, Helvetica, Geneva, sans-serif; font-size: 12px; transition: color 100ms ease 0s, opacity 100ms ease 0s; color: black; opacity: 1; left: 195px; right: auto; bottom: auto; top: 283px; visibility: inherit;">Z</div><div class="JXGtext" id="figure-box-0_jxgBoard1P6Label" display="inline" style="position: absolute; z-index: 9; font-family: Arial, Helvetica, Geneva, sans-serif; font-size: 12px; transition: color 100ms ease 0s, opacity 100ms ease 0s; color: black; opacity: 1; left: 289px; right: auto; bottom: auto; top: 112px; visibility: inherit;">Y</div><div class="JXGtext" id="figure-box-0_jxgBoard1P9Label" display="inline" style="position: absolute; z-index: 9; font-family: Arial, Helvetica, Geneva, sans-serif; font-size: 12px; transition: color 100ms ease 0s, opacity 100ms ease 0s; color: black; opacity: 1; left: 120px; right: auto; bottom: auto; top: 103px; visibility: inherit;">Q</div><div class="JXGtext" id="figure-box-0_jxgBoard1P12Label" display="inline" style="position: absolute; z-index: 9; font-family: Arial, Helvetica, Geneva, sans-serif; font-size: 12px; transition: color 100ms ease 0s, opacity 100ms ease 0s; color: black; opacity: 1; left: 15px; right: auto; bottom: auto; top: 267px; visibility: inherit;">D</div><div class="JXGtext" id="figure-box-0_jxgBoard1T18" display="inline" style="position: absolute; z-index: 9; font-family: Arial, Helvetica, Geneva, sans-serif; font-size: 12px; transition: color 100ms ease 0s, opacity 100ms ease 0s; color: black; opacity: 1; left: 198px; right: auto; bottom: auto; top: 220px; visibility: inherit;">56°</div><div class="JXGtext" id="figure-box-0_jxgBoard1T22" display="inline" style="position: absolute; z-index: 9; font-family: Arial, Helvetica, Geneva, sans-serif; font-size: 12px; transition: color 100ms ease 0s, opacity 100ms ease 0s; color: black; opacity: 1; left: 230px; right: auto; bottom: auto; top: 250px; visibility: inherit;">r</div><div class="JXGtext" id="figure-box-0_jxgBoard1T26" display="inline" style="position: absolute; z-index: 9; font-family: Arial, Helvetica, Geneva, sans-serif; font-size: 12px; transition: color 100ms ease 0s, opacity 100ms ease 0s; color: black; opacity: 1; left: 160px; right: auto; bottom: auto; top: 244px; visibility: inherit;">65°</div></div><p class="kLnDsmZC8c49r2Ntz8LHD"><span>Find the value of r in the given figure.</span></p><p class="kLnDsmZC8c49r2Ntz8LHD"><span></span></p></div><div></div></div></div>
  68.         </div></div></div><div class="horizontal-line__36CRY"></div><div class="solution-content__1ldKV"><div><div>
  69.             <style type="text/css">.kLnDsmZC8c49r2Ntz8LHD{display:table}._33s8iDB86ShboS4mZ56Q4l{width:100%}@media screen and (max-width:768px){.kLnDsmZC8c49r2Ntz8LHD{font-size:14px}}._1U4FJGd7TInh5eAPQAmzsY{width:inherit;display:table}._1U4FJGd7TInh5eAPQAmzsY ._2nYiFcHn-K_1fQeO_SGARi{display:table-row;flex-direction:row;justify-content:center;margin:1em 0}._1U4FJGd7TInh5eAPQAmzsY ._2nYiFcHn-K_1fQeO_SGARi ._1xHR7qH0lIQGdm-joycBuJ{padding:.5em;align-self:center;max-width:33.33%;display:table-cell;vertical-align:middle}._1U4FJGd7TInh5eAPQAmzsY ._2nYiFcHn-K_1fQeO_SGARi ._1xHR7qH0lIQGdm-joycBuJ p{text-align:left}._1U4FJGd7TInh5eAPQAmzsY ._2nYiFcHn-K_1fQeO_SGARi ._1xHR7qH0lIQGdm-joycBuJ:first-child{text-align:right}._1U4FJGd7TInh5eAPQAmzsY ._2nYiFcHn-K_1fQeO_SGARi ._1xHR7qH0lIQGdm-joycBuJ:last-child{text-align:left}._1U4FJGd7TInh5eAPQAmzsY ._2nYiFcHn-K_1fQeO_SGARi ._2S6gAwiBV5mgFpUS3zc_7W{white-space:nowrap;align-items:center}@media screen and (max-width:768px){._2nYiFcHn-K_1fQeO_SGARi{font-size:14px}}</style>
  70.             <div><div class="_33s8iDB86ShboS4mZ56Q4l"><div class="solution"><div></div><div class="_1U4FJGd7TInh5eAPQAmzsY"><div class="_2nYiFcHn-K_1fQeO_SGARi"><div class="_1xHR7qH0lIQGdm-joycBuJ _2S6gAwiBV5mgFpUS3zc_7W"><span><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mtext>r</mtext><mo>+</mo><mtext>56</mtext><mi mathvariant="normal">°</mi><mo>+</mo><mtext>65</mtext><mi mathvariant="normal">°</mi></mrow><annotation encoding="application/x-tex">\text{r}+\text{56}\degree+\text{65}\degree</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.69444em;"></span><span class="strut bottom" style="height:0.77777em;vertical-align:-0.08333em;"></span><span class="base"><span class="mord text"><span class="mord">r</span></span><span class="mord rule" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mord rule" style="margin-right:0.2222222222222222em;"></span><span class="mord text"><span class="mord">56</span></span><span class="mord">°</span><span class="mord rule" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mord rule" style="margin-right:0.2222222222222222em;"></span><span class="mord text"><span class="mord">65</span></span><span class="mord">°</span></span></span></span></span><span></span></div><div class="_1xHR7qH0lIQGdm-joycBuJ"> = </div><div class="_1xHR7qH0lIQGdm-joycBuJ"><span><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mtext>180</mtext><mi mathvariant="normal">°</mi><mo fence="false">(</mo><mtext>Sum&nbsp;of&nbsp;all&nbsp;adjacent&nbsp;angles&nbsp;on&nbsp;a&nbsp;straight&nbsp;line&nbsp;is&nbsp;180°</mtext><mo fence="false">)</mo></mrow><annotation encoding="application/x-tex">\text{180}\degree \big(\text{Sum of all adjacent angles on a straight line is 180\degree}\big)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.85em;"></span><span class="strut bottom" style="height:1.20001em;vertical-align:-0.35001em;"></span><span class="base"><span class="mord text"><span class="mord">180</span></span><span class="mord">°</span><span class="mord"><span class="delimsizing size1">(</span></span><span class="mord text"><span class="mord">Sum&nbsp;of&nbsp;all&nbsp;adjacent&nbsp;angles&nbsp;on&nbsp;a&nbsp;straight&nbsp;line&nbsp;is&nbsp;180°</span></span><span class="mord"><span class="delimsizing size1">)</span></span></span></span></span></span><span></span></div></div><div class="_2nYiFcHn-K_1fQeO_SGARi"><div class="_1xHR7qH0lIQGdm-joycBuJ _2S6gAwiBV5mgFpUS3zc_7W"><span><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mtext>r</mtext><mo>+</mo><mtext>121</mtext><mi mathvariant="normal">°</mi></mrow><annotation encoding="application/x-tex">\text{r}+\text{121}\degree</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.69444em;"></span><span class="strut bottom" style="height:0.77777em;vertical-align:-0.08333em;"></span><span class="base"><span class="mord text"><span class="mord">r</span></span><span class="mord rule" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mord rule" style="margin-right:0.2222222222222222em;"></span><span class="mord text"><span class="mord">121</span></span><span class="mord">°</span></span></span></span></span><span></span></div><div class="_1xHR7qH0lIQGdm-joycBuJ"> = </div><div class="_1xHR7qH0lIQGdm-joycBuJ"><span><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mtext>180</mtext><mi mathvariant="normal">°</mi></mrow><annotation encoding="application/x-tex">\text{180}\degree</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.69444em;"></span><span class="strut bottom" style="height:0.69444em;vertical-align:0em;"></span><span class="base"><span class="mord text"><span class="mord">180</span></span><span class="mord">°</span></span></span></span></span><span></span></div></div><div class="_2nYiFcHn-K_1fQeO_SGARi"><div class="_1xHR7qH0lIQGdm-joycBuJ _2S6gAwiBV5mgFpUS3zc_7W"><span><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mtext>r</mtext></mrow><annotation encoding="application/x-tex">\text{r}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.43056em;"></span><span class="strut bottom" style="height:0.43056em;vertical-align:0em;"></span><span class="base"><span class="mord text"><span class="mord">r</span></span></span></span></span></span><span></span></div><div class="_1xHR7qH0lIQGdm-joycBuJ"> = </div><div class="_1xHR7qH0lIQGdm-joycBuJ"><span><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mtext>180</mtext><mi mathvariant="normal">°</mi><mo>−</mo><mtext>121</mtext><mi mathvariant="normal">°</mi></mrow><annotation encoding="application/x-tex">\text{180}\degree-\text{121}\degree</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.69444em;"></span><span class="strut bottom" style="height:0.77777em;vertical-align:-0.08333em;"></span><span class="base"><span class="mord text"><span class="mord">180</span></span><span class="mord">°</span><span class="mord rule" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mord rule" style="margin-right:0.2222222222222222em;"></span><span class="mord text"><span class="mord">121</span></span><span class="mord">°</span></span></span></span></span><span></span></div></div><div class="_2nYiFcHn-K_1fQeO_SGARi"><div class="_1xHR7qH0lIQGdm-joycBuJ _2S6gAwiBV5mgFpUS3zc_7W"><span><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mtext>r</mtext></mrow><annotation encoding="application/x-tex">\text{r}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.43056em;"></span><span class="strut bottom" style="height:0.43056em;vertical-align:0em;"></span><span class="base"><span class="mord text"><span class="mord">r</span></span></span></span></span></span><span></span></div><div class="_1xHR7qH0lIQGdm-joycBuJ"> = </div><div class="_1xHR7qH0lIQGdm-joycBuJ"><span><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mtext>59</mtext><mi mathvariant="normal">°</mi></mrow><annotation encoding="application/x-tex">\text{59}\degree</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.69444em;"></span><span class="strut bottom" style="height:0.69444em;vertical-align:0em;"></span><span class="base"><span class="mord text"><span class="mord">59</span></span><span class="mord">°</span></span></span></span></span><span></span></div></div></div></div><div></div></div></div>
  71.         </div></div></div></div></div></div></div><div><div class="question-info-container__1jee9"><div class="question-heading-section__1U6d5"><div class="question-number__SpJ1d">Question 5</div><div class="content-button__3Q0iO">Show Content</div></div><div class="question-container__N3ddu"><div class="question-display-info__2bd0J"><div class="question-content__3NN6L"><div><div>
  72.             <style type="text/css">.kLnDsmZC8c49r2Ntz8LHD{display:table}._33s8iDB86ShboS4mZ56Q4l{width:100%}@media screen and (max-width:768px){.kLnDsmZC8c49r2Ntz8LHD{font-size:14px}}.mvBLLCQZNx56pwd5_Vazm,._1gd72wi83IbxAsemSie8HX{display:inline-block;-webkit-transform:scale(.5);transform:scale(.5);-webkit-transform-origin:0 bottom;transform-origin:0 bottom;height:400px;margin-top:-200px}@media screen and (min-width:741px){._1gd72wi83IbxAsemSie8HX{width:400px}.mvBLLCQZNx56pwd5_Vazm,._1gd72wi83IbxAsemSie8HX{height:400px;margin:10px;-webkit-transform:scale(1);transform:scale(1);-webkit-transform-origin:0;transform-origin:0}.mvBLLCQZNx56pwd5_Vazm{width:600px}}</style>
  73.             <div><div class="_33s8iDB86ShboS4mZ56Q4l"><div class="solution"><div id="figure-box-0" class="_1gd72wi83IbxAsemSie8HX" style="user-select: none; overflow: hidden; position: relative; touch-action: none;"><svg width="400" height="400" style="overflow: hidden; width: 400px; height: 400px;"><defs><filter id="figure-box-0_f1" width="300%" height="300%" filterUnits="userSpaceOnUse"><feOffset result="offOut" in="SourceAlpha" dx="5" dy="5"></feOffset><feGaussianBlur result="blurOut" in="offOut" stdDeviation="3"></feGaussianBlur><feBlend in="SourceGraphic" in2="blurOut" mode="normal"></feBlend></filter></defs><g></g><g></g><g></g><g><path id="figure-box-0_jxgBoard1G15" stroke-linecap="round" stroke-linejoin="round" stroke="#333" stroke-opacity="1" stroke-width="1px" fill="#fff" fill-opacity="0.3" d=" M 200.00000000000003 280.72194696821384 C 208.99100000000004 280.72194696821384 217.98200000000003 280.72194696821384 227.00000000000003 280.72194696821384 C 227.00000000000003 275.02010711653054 225.1949162238766 269.4646304955332 221.84345884812362 264.85174515631707 C 214.56958705169845 270.1365223596787 207.2957152552733 275.4212995630403 200.00000000000003 280.72194696821384" display="inline" style="position: absolute; 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transition: fill 100ms ease 0s, fill-opacity 100ms ease 0s, stroke 100ms ease 0s, stroke-opacity 100ms ease 0s; visibility: hidden;"></ellipse></g><g></g><g></g><g></g><g></g><g></g><g></g><g></g><g></g><g></g><g></g><foreignObject x="0" y="0" width="100%" height="100%" id="figure-box-0_foreignObj"></foreignObject></svg><div class="JXGinfobox" id="figure-box-0_jxgBoard1_infobox" display="none" style="position: absolute; z-index: 9; font-family: Arial, Helvetica, Geneva, sans-serif; font-size: 12px; color: rgb(187, 187, 187); opacity: 1; left: 200px; right: auto; bottom: auto; top: 280px; visibility: hidden;">0,0</div><div id="figure-box-0_navigationbar" class="JXG_navigation" style="color: rgb(51, 51, 51); background-color: transparent; padding: 2px; position: absolute; font-size: 14px; cursor: pointer; z-index: 100; right: 5px; bottom: 5px;"></div><div class="JXGtext" id="figure-box-0_jxgBoard1P1Label" display="inline" style="position: absolute; z-index: 9; font-family: Arial, Helvetica, Geneva, sans-serif; font-size: 12px; transition: color 100ms ease 0s, opacity 100ms ease 0s; color: black; opacity: 1; left: 377px; right: auto; bottom: auto; top: 274px; visibility: inherit;">D</div><div class="JXGtext" id="figure-box-0_jxgBoard1P3Label" display="inline" style="position: absolute; z-index: 9; font-family: Arial, Helvetica, Geneva, sans-serif; font-size: 12px; transition: color 100ms ease 0s, opacity 100ms ease 0s; color: black; opacity: 1; left: 187px; right: auto; bottom: auto; top: 288px; visibility: inherit;">F</div><div class="JXGtext" id="figure-box-0_jxgBoard1P6Label" display="inline" style="position: absolute; z-index: 9; font-family: Arial, Helvetica, Geneva, sans-serif; font-size: 12px; transition: color 100ms ease 0s, opacity 100ms ease 0s; color: black; opacity: 1; left: 343px; right: auto; bottom: auto; top: 167px; visibility: inherit;">H</div><div class="JXGtext" id="figure-box-0_jxgBoard1P9Label" display="inline" style="position: absolute; z-index: 9; font-family: Arial, Helvetica, Geneva, sans-serif; font-size: 12px; transition: color 100ms ease 0s, opacity 100ms ease 0s; color: black; opacity: 1; left: 227px; right: auto; bottom: auto; top: 95px; visibility: inherit;">G</div><div class="JXGtext" id="figure-box-0_jxgBoard1P12Label" display="inline" style="position: absolute; z-index: 9; font-family: Arial, Helvetica, Geneva, sans-serif; font-size: 12px; transition: color 100ms ease 0s, opacity 100ms ease 0s; color: black; opacity: 1; left: 15px; right: auto; bottom: auto; top: 274px; visibility: inherit;">P</div><div class="JXGtext" id="figure-box-0_jxgBoard1T18" display="inline" style="position: absolute; z-index: 9; font-family: Arial, Helvetica, Geneva, sans-serif; font-size: 12px; transition: color 100ms ease 0s, opacity 100ms ease 0s; color: black; opacity: 1; left: 234px; right: auto; bottom: auto; top: 263px; visibility: inherit;">36°</div><div class="JXGtext" id="figure-box-0_jxgBoard1T22" display="inline" style="position: absolute; z-index: 9; font-family: Arial, Helvetica, Geneva, sans-serif; font-size: 12px; transition: color 100ms ease 0s, opacity 100ms ease 0s; color: black; opacity: 1; left: 220px; right: auto; bottom: auto; top: 235px; visibility: inherit;">2x</div><div class="JXGtext" id="figure-box-0_jxgBoard1T26" display="inline" style="position: absolute; z-index: 9; font-family: Arial, Helvetica, Geneva, sans-serif; font-size: 12px; transition: color 100ms ease 0s, opacity 100ms ease 0s; color: black; opacity: 1; left: 163px; right: auto; bottom: auto; top: 237px; visibility: inherit;">100°</div></div><p class="kLnDsmZC8c49r2Ntz8LHD"><span>Find the value of x in the given figure.</span></p><p class="kLnDsmZC8c49r2Ntz8LHD"><span></span></p></div><div></div></div></div>
  74.         </div></div></div><div class="horizontal-line__36CRY"></div><div class="solution-content__1ldKV"><div><div>
  75.             <style type="text/css">.kLnDsmZC8c49r2Ntz8LHD{display:table}._33s8iDB86ShboS4mZ56Q4l{width:100%}@media screen and (max-width:768px){.kLnDsmZC8c49r2Ntz8LHD{font-size:14px}}._1U4FJGd7TInh5eAPQAmzsY{width:inherit;display:table}._1U4FJGd7TInh5eAPQAmzsY ._2nYiFcHn-K_1fQeO_SGARi{display:table-row;flex-direction:row;justify-content:center;margin:1em 0}._1U4FJGd7TInh5eAPQAmzsY ._2nYiFcHn-K_1fQeO_SGARi ._1xHR7qH0lIQGdm-joycBuJ{padding:.5em;align-self:center;max-width:33.33%;display:table-cell;vertical-align:middle}._1U4FJGd7TInh5eAPQAmzsY ._2nYiFcHn-K_1fQeO_SGARi ._1xHR7qH0lIQGdm-joycBuJ p{text-align:left}._1U4FJGd7TInh5eAPQAmzsY ._2nYiFcHn-K_1fQeO_SGARi ._1xHR7qH0lIQGdm-joycBuJ:first-child{text-align:right}._1U4FJGd7TInh5eAPQAmzsY ._2nYiFcHn-K_1fQeO_SGARi ._1xHR7qH0lIQGdm-joycBuJ:last-child{text-align:left}._1U4FJGd7TInh5eAPQAmzsY ._2nYiFcHn-K_1fQeO_SGARi ._2S6gAwiBV5mgFpUS3zc_7W{white-space:nowrap;align-items:center}@media screen and (max-width:768px){._2nYiFcHn-K_1fQeO_SGARi{font-size:14px}}</style>
  76.             <div><div class="_33s8iDB86ShboS4mZ56Q4l"><div class="solution"><div></div><div class="_1U4FJGd7TInh5eAPQAmzsY"><div class="_2nYiFcHn-K_1fQeO_SGARi"><div class="_1xHR7qH0lIQGdm-joycBuJ _2S6gAwiBV5mgFpUS3zc_7W"><span><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mtext>2x</mtext><mo>+</mo><mtext>36</mtext><mi mathvariant="normal">°</mi><mo>+</mo><mtext>100</mtext><mi mathvariant="normal">°</mi></mrow><annotation encoding="application/x-tex">\text{2x}+\text{36}\degree+\text{100}\degree</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.69444em;"></span><span class="strut bottom" style="height:0.77777em;vertical-align:-0.08333em;"></span><span class="base"><span class="mord text"><span class="mord">2x</span></span><span class="mord rule" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mord rule" style="margin-right:0.2222222222222222em;"></span><span class="mord text"><span class="mord">36</span></span><span class="mord">°</span><span class="mord rule" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mord rule" style="margin-right:0.2222222222222222em;"></span><span class="mord text"><span class="mord">100</span></span><span class="mord">°</span></span></span></span></span><span></span></div><div class="_1xHR7qH0lIQGdm-joycBuJ"> = </div><div class="_1xHR7qH0lIQGdm-joycBuJ"><span><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mtext>180</mtext><mi mathvariant="normal">°</mi><mo fence="false">(</mo><mtext>Sum&nbsp;of&nbsp;all&nbsp;adjacent&nbsp;angles&nbsp;on&nbsp;a&nbsp;straight&nbsp;line&nbsp;is&nbsp;180°</mtext><mo fence="false">)</mo></mrow><annotation encoding="application/x-tex">\text{180}\degree \big(\text{Sum of all adjacent angles on a straight line is 180\degree}\big)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.85em;"></span><span class="strut bottom" style="height:1.20001em;vertical-align:-0.35001em;"></span><span class="base"><span class="mord text"><span class="mord">180</span></span><span class="mord">°</span><span class="mord"><span class="delimsizing size1">(</span></span><span class="mord text"><span class="mord">Sum&nbsp;of&nbsp;all&nbsp;adjacent&nbsp;angles&nbsp;on&nbsp;a&nbsp;straight&nbsp;line&nbsp;is&nbsp;180°</span></span><span class="mord"><span class="delimsizing size1">)</span></span></span></span></span></span><span></span></div></div><div class="_2nYiFcHn-K_1fQeO_SGARi"><div class="_1xHR7qH0lIQGdm-joycBuJ _2S6gAwiBV5mgFpUS3zc_7W"><span><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mtext>2x</mtext><mo>+</mo><mtext>136</mtext><mi mathvariant="normal">°</mi></mrow><annotation encoding="application/x-tex">\text{2x}+\text{136}\degree</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.69444em;"></span><span class="strut bottom" style="height:0.77777em;vertical-align:-0.08333em;"></span><span class="base"><span class="mord text"><span class="mord">2x</span></span><span class="mord rule" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mord rule" style="margin-right:0.2222222222222222em;"></span><span class="mord text"><span class="mord">136</span></span><span class="mord">°</span></span></span></span></span><span></span></div><div class="_1xHR7qH0lIQGdm-joycBuJ"> = </div><div class="_1xHR7qH0lIQGdm-joycBuJ"><span><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mtext>180</mtext><mi mathvariant="normal">°</mi></mrow><annotation encoding="application/x-tex">\text{180}\degree</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.69444em;"></span><span class="strut bottom" style="height:0.69444em;vertical-align:0em;"></span><span class="base"><span class="mord text"><span class="mord">180</span></span><span class="mord">°</span></span></span></span></span><span></span></div></div><div class="_2nYiFcHn-K_1fQeO_SGARi"><div class="_1xHR7qH0lIQGdm-joycBuJ _2S6gAwiBV5mgFpUS3zc_7W"><span><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mtext>2x</mtext></mrow><annotation encoding="application/x-tex">\text{2x}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.64444em;"></span><span class="strut bottom" style="height:0.64444em;vertical-align:0em;"></span><span class="base"><span class="mord text"><span class="mord">2x</span></span></span></span></span></span><span></span></div><div class="_1xHR7qH0lIQGdm-joycBuJ"> = </div><div class="_1xHR7qH0lIQGdm-joycBuJ"><span><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mtext>180</mtext><mi mathvariant="normal">°</mi><mo>−</mo><mtext>136</mtext><mi mathvariant="normal">°</mi></mrow><annotation encoding="application/x-tex">\text{180}\degree-\text{136}\degree</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.69444em;"></span><span class="strut bottom" style="height:0.77777em;vertical-align:-0.08333em;"></span><span class="base"><span class="mord text"><span class="mord">180</span></span><span class="mord">°</span><span class="mord rule" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mord rule" style="margin-right:0.2222222222222222em;"></span><span class="mord text"><span class="mord">136</span></span><span class="mord">°</span></span></span></span></span><span></span></div></div><div class="_2nYiFcHn-K_1fQeO_SGARi"><div class="_1xHR7qH0lIQGdm-joycBuJ _2S6gAwiBV5mgFpUS3zc_7W"><span><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mtext>2x</mtext></mrow><annotation encoding="application/x-tex">\text{2x}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.64444em;"></span><span class="strut bottom" style="height:0.64444em;vertical-align:0em;"></span><span class="base"><span class="mord text"><span class="mord">2x</span></span></span></span></span></span><span></span></div><div class="_1xHR7qH0lIQGdm-joycBuJ"> = </div><div class="_1xHR7qH0lIQGdm-joycBuJ"><span><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mtext>44</mtext><mi mathvariant="normal">°</mi></mrow><annotation encoding="application/x-tex">\text{44}\degree</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.69444em;"></span><span class="strut bottom" style="height:0.69444em;vertical-align:0em;"></span><span class="base"><span class="mord text"><span class="mord">44</span></span><span class="mord">°</span></span></span></span></span><span></span></div></div><div class="_2nYiFcHn-K_1fQeO_SGARi"><div class="_1xHR7qH0lIQGdm-joycBuJ _2S6gAwiBV5mgFpUS3zc_7W"><span><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mtext>x</mtext></mrow><annotation encoding="application/x-tex">\text{x}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.43056em;"></span><span class="strut bottom" style="height:0.43056em;vertical-align:0em;"></span><span class="base"><span class="mord text"><span class="mord">x</span></span></span></span></span></span><span></span></div><div class="_1xHR7qH0lIQGdm-joycBuJ"> = </div><div class="_1xHR7qH0lIQGdm-joycBuJ"><span><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mfrac><mrow><mtext>44</mtext><mi mathvariant="normal">°</mi></mrow><mrow><mtext>2</mtext></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{\text{44}\degree}{\text{2}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.8801079999999999em;"></span><span class="strut bottom" style="height:1.2251079999999999em;vertical-align:-0.345em;"></span><span class="base"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8801079999999999em;"><span style="top:-2.6550000000000002em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">2</span></span></span></span></span><span style="top:-3.15em;"><span class="pstrut" style="height:3em;"></span><span class="stretchy" style="height:0.2em;"><svg width="400em" height="0.2em" viewBox="0 0 400000 200" preserveAspectRatio="xMinYMin slice"><path d="M0 80H400000 v40H0z M0 80H400000 v40H0z"></path></svg></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord mtight">44</span></span><span class="mord mtight">°</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span><span></span></div></div><div class="_2nYiFcHn-K_1fQeO_SGARi"><div class="_1xHR7qH0lIQGdm-joycBuJ _2S6gAwiBV5mgFpUS3zc_7W"><span><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mtext>x</mtext></mrow><annotation encoding="application/x-tex">\text{x}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.43056em;"></span><span class="strut bottom" style="height:0.43056em;vertical-align:0em;"></span><span class="base"><span class="mord text"><span class="mord">x</span></span></span></span></span></span><span></span></div><div class="_1xHR7qH0lIQGdm-joycBuJ"> = </div><div class="_1xHR7qH0lIQGdm-joycBuJ"><span><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mtext>22</mtext><mi mathvariant="normal">°</mi></mrow><annotation encoding="application/x-tex">\text{22}\degree</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.69444em;"></span><span class="strut bottom" style="height:0.69444em;vertical-align:0em;"></span><span class="base"><span class="mord text"><span class="mord">22</span></span><span class="mord">°</span></span></span></span></span><span></span></div></div></div></div><div></div></div></div>
  77.         </div></div></div></div></div></div></div><div class="page-number-wrapper__1b9Mc"><div><div class="page-number-container__38kvK"><div class="page-container__1icC4"><div class="page-numbers-list__2zB60" style="transform: translateX(0px);"><div class="page-number__1QMO1 current-page__EDprS">Page 1</div><div class="page-number__1QMO1 ">Page 2</div><div class="page-number__1QMO1 ">Page 3</div></div></div></div></div></div></div></div></div></div></div></div></div><script src="/bundle.mlm6m04vf78qklspjvigv.js" async=""></script><script src="/teacherdashboard.mlm6m04vf78qklspjvigv.js" defer="defer"></script><script>const JWT_KEY = 'cerebry-jwt-token';
  78.   const JWT_REFRESH = 'cerebry-jwt-refresh';
  79.  
  80.   var Cerebry = window.Cerebry || {};
  81.   Cerebry.init = function (params) {
  82.     Object.assign(Cerebry, params);
  83.     const script = document.createElement('script')
  84.     script.src = `/bundle.mlm6m04vf78qklspjvigv.js`;
  85.     script.async = true
  86.     const entry = document.getElementsByTagName("script")[0]
  87.     entry.parentNode.insertBefore(script, entry)
  88.   }
  89.  
  90.   function handle401() {
  91.     try {
  92.       refreshUser(getJwtToken(JWT_REFRESH))
  93.       .then(response => {
  94.         window.location.setItem(JWT_KEY, response.jwt);
  95.         showSpark(response.jwt,getJwtToken(JWT_REFRESH));
  96.       })
  97.       .catch(error => {
  98.         window.localStorage.removeItem(JWT_KEY);
  99.         window.localStorage.removeItem(JWT_REFRESH);
  100.         showSpark();
  101.       })
  102.     }catch(e) {
  103.       window.localStorage.removeItem(JWT_KEY);
  104.       window.localStorage.removeItem(JWT_REFRESH);
  105.       showSpark();
  106.     }
  107.   }
  108.  
  109.   function refreshUser(jwt) {
  110.     return new Promise((resolve, reject) => {
  111.       const xhttp = new XMLHttpRequest();
  112.       xhttp.onreadystatechange = function () {
  113.         if (this.readyState == 4 && this.status == 200) {
  114.          const response = JSON.parse(xhttp.responseText);
  115.           resolve(response);
  116.         } else if (this.readyState == 4 && this.status >= 400) {
  117.          const error = JSON.parse(xhttp.responseText);
  118.           reject(error);
  119.         }
  120.       };
  121.       xhttp.open("POST", 'https://staging.sparkbackend.cerebry.co/api/v2/users/refresh/', true);
  122.       xhttp.setRequestHeader("Authorization", "jwt "+jwt);
  123.       xhttp.send();
  124.     })
  125.   }
  126.  
  127.   function showDashboard(jwt, jwtRefresh) {
  128.     if(document.getElementsByClassName("teacher-dashboard").length <= 0) {
  129.      var app = document.createElement('div');
  130.      app.setAttribute("class", "teacher-dashboard");
  131.      app.setAttribute("cerebry-widget-host", "teacher-dashboard");
  132.      document.getElementById("app").appendChild(app);
  133.  
  134.      Cerebry.init({
  135.        jwt_token: jwt,
  136.        jwt_refresh: jwtRefresh,
  137.        failedAuthCB: function () {
  138.          handle401();
  139.        }
  140.      });
  141.    }
  142.  }
  143.  
  144.  function getJwtToken(jwtToken) {
  145.    return window.localStorage.getItem(jwtToken);
  146.  }
  147.  
  148.  async function windowOnLoad() {
  149.    await window.removeEventListener("load", windowOnLoad);
  150.    await showDashboard(getJwtToken(JWT_KEY), getJwtToken(JWT_REFRESH));
  151.  }
  152.  
  153.  window.addEventListener("load", windowOnLoad);</script><script src="https://cerebry-third-party.s3-ap-southeast-1.amazonaws.com/answer-extraction.min.js"></script><script type="text/javascript" async="" src="https://cerebry-third-party.s3-ap-southeast-1.amazonaws.com/parse_answer.1.0.0.min.js"></script></body></html>
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