Question

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

1. m∠PRT
2. m∠P
3. m∠Q

Answer 1

(i) ∠PRQ + ∠PRT = 180^∘   ...(Linear pair angles)

⇒ 70° +  ∠PRT = 180°

⇒ ∠PRT = 180^∘ − 70°

= 110^∘

Hence, the measure of ∠PRT is 110^∘​.

(ii) Now, ∠PRT is the exterior angle of ∆PQR.

∴ m∠P + m∠Q = m∠PRT   ...(Exterior angle property)

∴ m∠P + m∠P = 110    ...(∠P = ∠Q)

∴ 2m∠P = 110

∴ m∠P = `110/2`

∴ m∠P = 55°

(iii) In ΔPQR

∴ m∠P + m∠Q = m∠PRT   ...(Exterior angle property)

∴ m∠Q + m∠Q = 110    ...(∠P = ∠Q)

∴ 2m∠Q = 110

∴ m∠Q = `110/2`

∴ m∠Q = 55°