Given,
⇒ ∠PQR = ∠PRQ = x (let)
From figure,
⇒ ∠PQS + ∠PQR = 180° (Linear pair)
⇒ ∠PQS = 180° - ∠PQR
⇒ ∠PQS = 180° - x .......(1)
From figure,
⇒ ∠PRT + ∠PRQ = 180°
⇒ ∠PRT = 180° - ∠PRQ
⇒ ∠PRT = 180° - x .........(2)
From equations, (1) and (2) we get :
⇒ ∠PQS = ∠PRT
Hence, proved ∠PQS = ∠PRT.