3.  In Fig. 6.15, $\angle$ PQR = $\angle$ PRQ, then prove that $\angle$ PQS = $\angle$ PRT.

M manish painkra

Given that,
ABC is a triangle such that $\angle$ PQR = $\angle$ PRQ  and ST is a straight line.
Now, $\angle$ PQR + $\angle$ PQS = $180^0$     {Linear pair}............(i)
Similarly, $\angle$ PRQ + $\angle$ PRT = $180^0$..................(ii)

equating the eq (i) and eq (ii), we get

$\angle PQR +\angle PQS =\angle PRT + \angle PRQ$   {but $\angle$ PQR = $\angle$ PRQ }
Therefore, $\angle$ PQS = $\angle$ PRT
Hence proved.

Exams
Articles
Questions