Question

this triangle has an exterior angle labeled ∠a. all of the interior angles are labeled correctly. which statement about the exterior angle is correct? a. it is 140° because it is supplementary to 40°. b. it is 50° because it is complementary to 40°. c. it is 60° because 60°+40° = 100°. d. it is 120° because 40°+80° = 120°.

Explanation:

Step1: Recall angle - supplementary property

Two angles are supplementary if their sum is 180°.

Step2: Calculate the measure of ∠A

Let the measure of ∠A be \(x\). We know that the angle adjacent to ∠A is 40°. Since \(x + 40^{\circ}=180^{\circ}\), then \(x = 180^{\circ}-40^{\circ}=140^{\circ}\).

Answer:

A. It is 140° because it is supplementary to 40°.