Question

complete this sentence with the best of the choices given. if the exterior sides of adjacent angles are perpendicular, the angles are ________. after you pick your answer press go. a. complementary b. congruent c. supplementary d. acute e. a linear pair

Explanation:

Step1: Recall angle - relationship definitions

Let the two adjacent angles be $\angle A$ and $\angle B$. The exterior sides of adjacent angles being perpendicular means the angle formed by the non - common exterior sides is $90^{\circ}$.

Step2: Use the property of adjacent angles

The sum of the two adjacent angles $\angle A+\angle B + 90^{\circ}=180^{\circ}$ (since they form a straight - line or a linear - pair of angles with the right - angle between the exterior sides).

Step3: Solve for the sum of the two adjacent angles

Subtract $90^{\circ}$ from both sides of the equation $\angle A+\angle B+90^{\circ}=180^{\circ}$. We get $\angle A+\angle B = 90^{\circ}$.
Two angles whose sum is $90^{\circ}$ are complementary. So if the exterior sides of adjacent angles are perpendicular, the angles are complementary.

Answer:

A. complementary