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

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#### Solution

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

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