What is the value of $\angle PQR$ if  $PQRS$is cyclic quadrilateral and $PS=SR$?

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˚.

Since angles opposite to equal sides are equal,

In  $\Delta PSR,PS=PR\Rightarrow \angle PRS=\angle SPR={20}^{°}$By angle sum property of triangle,

Now,  $\angle PSR+\angle SPR+\angle SRP={180}^{°}$

$\Rightarrow \angle PSR+{20}^{°}+{20}^{°}={180}^{°}$

$\Rightarrow \angle PSR={140}^{°}$

Here,  $PQRS$ is a cyclic quadrilateral.

$\begin{array}{l}\Rightarrow \angle PQR+\angle PSR={180}^{°}\\ \Rightarrow \angle PQR={40}^{°}\end{array}$

Then, sum of any pair of opposite angles of cyclic quadrilateral is${180}^{°}$.

Hence, the value of $\angle PQR={40}^{°}$