Question:
In Figure, \(∠\)PQR = \(∠\)PRQ, then prove that \(∠\)PQS = \(∠\)PRT.
In Figure, \(∠\)PQR = \(∠\)PRQ, then prove that \(∠\)PQS = \(∠\)PRT.
Updated On: Jan 20, 2026
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Solution and Explanation
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 = 180º− \(∠\)PRT
\(∠\)PQS = \(∠\)PRT
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