Question

question 2 | module 2 review-angles and geometric figures. if (mangle2 = 108^{circ}), then the measure of the adjacent angle is select choice degrees and the measure of the vertical angle is select choice degrees.

Explanation:

Step1: Recall adjacent - angle property

Adjacent angles on a straight - line sum to 180°. Let the adjacent angle to ∠2 be ∠1. So, $m\angle1=180^{\circ}-m\angle2$.

Step2: Calculate the measure of the adjacent angle

Substitute $m\angle2 = 108^{\circ}$ into the formula: $m\angle1=180 - 108=72^{\circ}$.

Step3: Recall vertical - angle property

Vertical angles are equal. The vertical angle to ∠2 is ∠4. So, $m\angle4=m\angle2 = 108^{\circ}$.

Answer:

The measure of the adjacent angle is 72 degrees and the measure of the vertical angle is 108 degrees.