Question

In the given figure, $\angle PQR=\angle PRQ$, then prove that $\angle PQS=\angle PRT$

Answer 1

$\angle PQR=\angle PRQ\left(1\right)$ (Given)

$\angle PQS+\angle PQR={180}^{\circ }\left(2\right)$ (Linear pair property)

$\angle PQR+\angle PTR={180}^{\circ }\left(3\right)$ (By Linear pair property )

From (2) & (3)

$\angle PQS+\angle PQR=\angle PRQ+\angle PRT$

$\Rightarrow \angle PQS+\angle PQR=\angle PQR+\angle PRT$ 9From 1)

$\Rightarrow \angle PQS=\angle PRT$ (Proved)