Question

Two angles in triangle PQR are congruent, ∠P and ∠Q; ∠R measures 26.35°. What is the measure of ∠P?

127.3°
153.65°
26.35°
76.825°

Answer 1

The sum of all the three angles of a triangle is 180°.

x + x + 26.35° = 180°

2x = 180° - 26.35°

x = 76.825°.

Therefore, ∠P will be equal to 76.825°.

Answer 2

∠P = 76.825°

Explanation:

If angles P and Q are congruent, then triangle PQR is an isosceles triangle where ∠P and ∠Q are the base angles and ∠R is the apex angle.

The interior angles of a triangle sum to 180°. Therefore:

⇒ ∠P + ∠Q + ∠R = 180°

As ∠P = ∠Q and ∠R = 26.35°, then:

⇒ ∠P + ∠P + 26.35° = 180°

⇒ 2∠P + 26.35° = 180°

⇒ 2∠P + 26.35° - 26.35° = 180° - 26.35°

⇒ 2∠P = 153.65°

⇒ 2∠P ÷ 2 = 153.65° ÷ 2

⇒ ∠P = 76.825°

Therefore, the measure of angle P is 76.825°.