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In the given figure, $\angle PQR=\angle PRT$. Prove that $\angle PQS=\angle PRT$.
"
Given: $\angle PQR=\angle PRQ$
To do: To prove $\angle PQS=\angle PRT$
Solution:
$\angle PQR +\angle PQS =180^{\circ}$
$\angle PQS =180^{\circ}-\angle PQR\ ............( i)$
$\angle PRQ +\angle PRT=180^{\circ}$
$\angle PRT=180^{\circ}-\angle PRQ$
$\angle PRQ=180^{\circ}-\angle PQR\ .........( ii)$ [$\angle PQR=\angle PRQ$]
From $( i)$ and $( ii)$
$\angle PQS=\angle PRT=180^{\circ}-\angle PQR$
$\angle PQS=\angle PRT$
Hence, $\angle PQS=\angle PRT$
Updated on: 10-Oct-2022
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