Question

In the figure, sides $QP$ and $RQ$ of $\Delta PQR$ are produced to points $S$ and $T$ respectively. If $\angle SPR={135}^o$ and $\angle PQT={110}^o$, find $\angle PRQ$.

Answer 1

Given, $\angle SPR={135}^{\circ },\angle PQT={110}^{\circ }$
According to the question

$\angle SPR+\angle QPR={180}^{\circ }$ ($SQ$ is a straight line.)

$\Rightarrow {135}^{\circ }+\angle QPR={180}^{\circ }$

$\Rightarrow \angle QPR={45}^{\circ }$

Also $\angle PQT+\angle PQR={180}^{\circ }$ ($TR$ is a straight line.)

$\Rightarrow {110}^{\circ }+\angle PQR={180}^{\circ }$

$\Rightarrow \angle PQR={70}^{\circ }$

Now, $\angle PQR+\angle QPR+\angle PRQ={180}^{\circ }$ (Sum of the interior angles of the triangle.)

$\angle {70}^{\circ }+{45}^{\circ }+\angle PRQ={180}^{\circ }$

$\Rightarrow {115}^{\circ }+\angle PRQ={180}^{\circ }$

$\Rightarrow \angle PRQ={65}^{\circ }$