Question

In the given figure, sides QP and RQ of ΔPQR are produced to points * and T respectively. If ∠SPR = 135 and ∠PQT = 110, find ∠PRQ.

Answer 1

It is given that,

∠SPR = 135 and ∠PQT = 110

∠SPR + ∠QPR = 180 (Linear pair angles)

135 + ∠QPR = 180

∠QPR = 45

Also, ∠PQT + ∠PQR = 180 (Linear pair angles)

110 + ∠PQR = 180

∠PQR = 70

As the sum of all interior angles of a triangle is 180, therefore, for ΔPQR,

∠QPR + ∠PQR + ∠PRQ = 180

45 + 70 + ∠PRQ = 180

∠PRQ = 180 − 115

∠PRQ = 65