In the given figure, ST is a straight line and ray QP stands on it.

∴ ∠PQS + ∠PQR = 180º (Linear Pair)

∠PQR = 180º − ∠PQS (1)

∠PRT + ∠PRQ = 180º (Linear Pair)

∠PRQ = 180º − ∠PRT (2)

It is given that ∠PQR = ∠PRQ.

Equating equations (1) and (2), we obtain

180º − ∠PQS = 180 − ∠PRT

∠PQS = ∠PRT