In Fig. ∠PQR = ∠PRQ, then prove that ∠PQS = ∠PRT.

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.