Question

Two angles in triangle PQR are congruent, ∠P and ∠Q; ∠R measures 34.15°. What is the measure of ∠P?

145.85°
57.45°
34.15°
72.925°

Answer 1

(d) 72.925°

Explanation:

You have congruent angles P and Q in triangle PQR, where angle R measures 34.15°. You want to know the measure of angle P.

Angle sum theorem

The angle sum theorem tells you the sum of angles in a triangle is 180°.

P +Q +R = 180°

P +P +34.15° = 180° . . . . . substitute equivalents

2P = 145.85° . . . . . . . . . subtract 34.15°

P = 72.925° . . . . . . . . divide by 2

The measure of ∠P is 72.925°.