1.

Arc M-P = 70 degrees
Arc Q-M has to equal 110 degrees if Line Q-P is in the center of the circle
The measure of an inscribed angle in a circle is equal to one half the measure of the intercepted arc.
Line N-M is in the center of the circle which means...

Arc R-P = 70 degrees
arc Q-N = 110 degrees

Angle QMN = 55 degrees


2.

a. angle X = 110 degrees
angle Z = 70 degrees; 110+70=180

b. if arc w-x + arc x-y = 110 then arc w-y = 250
if w-z and y-z are equal then 250/2 = 125
arc W-Z = 125

3. 1-cos^2 x can not be simplified