Question

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

Answer 1

$\angle PQT+\angle PQR={180}^{\circ }$ (Straight angle made on line $TR$ at point $Q$)

${110}^{\circ }+\angle PQR{=180}^{\circ }\angle PQR{=180}^{\circ }-{110}^{\circ }={70}^{\circ }$

In $△PQR$

$\angle PSR=\angle PQR+\angle PRQ$ (Exterior angle of triangle is eqal to sum of two interior angles)

${135}^{\circ }={70}^{\circ }+\angle PRQ\angle PRQ={135}^{\circ }-{70}^{\circ }={65}^{\circ }$