Question

In Fig6.39 sides $QP$ and $RQ$ of $△PQR$ are proudued to points $S$ and $T$ respectively. If $\angle SPR={135}^o$ and $\angle PQT={110}^o$, find $\angle PRQ$

Answer 1

$\angle SPR={135}^o$ and $\angle PQT={110}^o$

Now,

$\angle SPR+\angle QPR={180}^o$

$\angle QPR={180}^o-{135}^o={45}^o$

Also,

$\angle PQT+\angle PQR={180}^o$

$\angle PQR={70}^o$

Now, in $△PQR$,

$\angle QPR+\angle PQR+\angle PRQ={180}^o$

$\angle PRQ={180}^o-{45}^o-{70}^o={65}^o$