In the figure,if $\angle PQR = \angle PRQ$,then prove that $\angle PQS = \angle PRT$.
(N/A) Since $ST$ is a straight line,
$\therefore \angle PQS + \angle PQR = 180^\circ$ ........... $(1)$
Similarly,$\angle PRT + \angle PRQ = 180^\circ$ ........... $(2)$
From $(1)$ and $(2)$,we have
$\angle PQS + \angle PQR = \angle PRT + \angle PRQ$
But $\angle PQR = \angle PRQ$ [Given]
$\therefore \angle PQS = \angle PRT$
$\therefore \angle PQS + \angle PQR = 180^\circ$ ........... $(1)$
Similarly,$\angle PRT + \angle PRQ = 180^\circ$ ........... $(2)$
From $(1)$ and $(2)$,we have
$\angle PQS + \angle PQR = \angle PRT + \angle PRQ$
But $\angle PQR = \angle PRQ$ [Given]
$\therefore \angle PQS = \angle PRT$
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