In the figure, ∠PQR = ∠PRQ, then prove that ∠PQS = ∠PRT

As Given, ∠PQR = ∠PRQ
To prove: ∠PQS = ∠PRT
According to the question, ∠PQR + ∠PQS = 180° Linear Pair
⇒ ∠PQS = 180° - ∠PQR — (i)
Also ∠PRQ + ∠PRT = 180° Linear Pair
⇒∠PRT = 180° - ∠PRQ
⇒∠PRQ = 180° - ∠PQR — (ii) (∠PQR = ∠PRQ)
From (i) and (ii), ∠PQS = ∠PRT = 180° - ∠PQR
∴ ∠PQS = ∠PRT [hence proved]