Question

If $PQRS$ is a cyclic quadrilateral in which $\angle PSR={70}^{\circ }$ and $\angle QPR={40}^{\circ }$, then find $\angle PRQ$.

Answer 1

$PQRS$ is a cyclic quadrilateral
Given $\angle PSR={70}^{\circ }$
$\begin{array}{cc}\angle PSR+\angle PQR& ={180}^{\circ }\\ {70}^{\circ }+\angle PQR& ={180}^{\circ }\\ \angle PQR& ={180}^{\circ }-{70}^{\circ }\\ \angle PQR& ={110}^{\circ }\end{array}$
In $△PQR$ we have,
$\begin{array}{cc}\angle PQR+\angle PRQ+\angle QPR& ={180}^{\circ }\\ {110}^{\circ }+\angle PRQ+{40}^{\circ }& ={180}^{\circ }\\ \angle PRQ& ={180}^{\circ }-{150}^{\circ }\\ \angle PRQ& ={30}^{\circ }\end{array}$