Question

a triangle has an interior angle labeled 40°. 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 130° because 40° + 90° = 130°.

Explanation:

Step1: Recall the exterior angle theorem

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles.

Step2: Identify the non - adjacent interior angles

The two non - adjacent interior angles to the exterior angle \(x\) are \(50^{\circ}\) and \(80^{\circ}\).

Step3: Calculate the exterior angle

Using the exterior angle theorem, \(x=50^{\circ}+80^{\circ}\).

$$x = 130^{\circ}$$

Answer:

D. It is \(130^{\circ}\) because \(50^{\circ}+80^{\circ}=130^{\circ}\)