Question

An exterior angle of a triangle is 152°. If the non-adjacent angles are congruent, then what are the measures of all of the interior angles of the triangle?

a. 62°, 59°, 59°
b. 90°, 45°, 45°
c. 152°, 14°, 14°
d. 28°, 76°, 76°

Answer 1

9514 1404 393

Answer:

d. 28°, 76°, 76°

Explanation:

The sum of the "non-adjacent" interior angles of the triangle is equal to the exterior angle, so is 152°. If those angles are congruent, each is half of 152°, or 76°. The remaining angle is the supplement to 152°, so is 180-152 = 28 degrees.

The interior angles are 28°, 76°, 76°.