In the given figure, ST is a straight line and ray QP stands on it.
∴∠PQS+∠PQR=180∘ ( Linear Pair)
∠PQR=180∘−∠PQS……………..(1)
∠PRT+∠PRQ=180∘ (Linear pair)
∠PRQ=180∘−∠PRT……………(2)
It is given that ∠PQR=∠PRQ.
Equating equations (1) and (2), we obtain,
180∘−∠PQS=180∘−∠PRT
∠PQS=∠PRT