Question

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

Answer 1

Given: ∠PQR = ∠PRQ

To prove: ∠PQS = ∠PRT

Proof:

∠PQS + ∠PQR = 180°            ...(1) Linear pair

∠PRT + ∠PRQ = 180°            ...(2) Linear pair

From equations (1) and (2)

∠PQS + ∠PQR = ∠PRT + ∠PRQ

or, ∠PQS + ∠PQR = ∠PRT + ∠PQR        ...(∠PQR = ∠PRQ is given)

or, ∠PQS + ∠PQR = ∠PRT + ∠PQR

or ∠PQS = ∠PRT is proved.