Question

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

Answer 1

As Given, $\angle PQR=\angle PRQ$

To prove: $\angle PQS=\angle PRT$

According to the question,

$\angle PQR+\angle PQS={180}^{\circ }$ $\mid$ Linear Pair

$\Rightarrow \angle PQS={180}^{\circ }-\angle PQR$--- (i)

Also $\angle PRQ+\angle PRT={180}^{\circ }$ $\mid$ Linear Pair

$\Rightarrow PRT={180}^{\circ }-\angle PRQ$

$\Rightarrow \angle PRQ={180}^{\circ }-\angle PQR---\left(ii\right)$$(\angle PQR=\angle PRQ)$

From (i) and (ii),

$\angle PQS=\angle PRT={180}^{\circ }-\angle PQR$

$\therefore \angle PQS=\angle PRT$ $\left[henceproved\right]$