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

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Solution

Given: $∠$ PQR = $∠$ PRQ
Since ST is a straight line, so
$∠ P Q S = 180^{\circ} - ∠ P Q R = 180^{\circ} - ∠ P R Q (∵ ∠ P R Q = ∠ P Q R) = ∠ P R T$
Hence, $∠ P Q S = ∠ P R T$ .

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