Find the value of $\angle PQR$ if  $PS\left|\right|RQ$ and $PQRS$is cyclic quadrilateral.

Concept: Every angle of a cyclic quadrilateral is on a circle (circumscribed circle), and the sum of any two opposite angles of a cyclic quadrilateral is 180˚.

Here, $PQRS$is a cyclic quadrilateral.

Then, sum of any pair of opposite angles of cyclic quadrilateral is 180˚.

$\begin{array}{l}\Rightarrow \angle P+\angle R={180}^{°}\\ \Rightarrow \angle P={100}^{°}\end{array}$

By sum of interior angles property,

Now, $PS\left|\right|RQ\Rightarrow \angle SPQ+\angle PQR={180}^{°}$

$\Rightarrow \angle PQR+{100}^{°}={180}^{°}$

$\Rightarrow \angle PQR={80}^{°}$

Hence, the value of $\angle PQR={80}^{°}$