Question

figure

In ∆PQR, the measures of $\angle$P and $\angle$Q are equal and m$\angle$PRQ = 70^°. Find the measures of the following angles.

(i) m$\angle$PRT (ii) m$\angle$P (iii) m$\angle$Q

Answer 1

(i)
∠PRQ + ∠PRT = 180^∘ (Linear pair angles)
⇒ ∠PRT = 180^∘ − 70^∘
= 110^∘
Hence, the measure of ∠PRT is 110^∘​.

(ii)

In ΔPQR,
∠P + ∠Q = ∠PRT (Exterior angle property)
⇒ ∠P + ∠P = 110^∘ (∠P = ∠Q)
⇒ 2∠P = 110^∘
⇒ ∠P = 55^∘
Hence, the measure of ∠P is 55^∘​.

(iii)

In ΔPQR,
∠P + ∠Q = ∠PRT (Exterior angle property)
⇒ ∠Q + ∠Q = 110^∘ (∠P = ∠Q)
⇒ 2∠Q = 110^∘
⇒ ∠Q = 55^∘
Hence, the measure of ∠Q is 55^∘​.