<select ng-model="$ctrl.type">
    <option value="">none</option>
    <option value="1">1</option>
    <option value="2">2</option>
</select>

<div ng-show="ctrl.type!=""" class="btn action-btn" ng-click="$ctrl.doSomething()">
        my button
    </div>

doSomething() {
    this.type = "";
}

<div ng-show="ctrl.type!="''" class="btn action-btn" ng-click="$ctrl.doSomething()">