Question

In fig, sides $QP$ and $RQ$ of triangle $PQR$ are produced to point $S$ and $T$ respectively. If angle $SPR={135}^{\circ }$ and angle $PQT={110}^{\circ }\text{,find}\angle PRQ$.

Answer 1

REF.Image

So:- $\angle PQT+\angle PQR=180$

$110+\angle PQR=180$

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

Now, $\angle SPR+\angle QPR=180$

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

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

Now,

$\angle QPR+\angle PQR+\angle QRP=180$

$45+70+\angle QRP=180$

$\angle QRP=65$