Choose the correct option:

PQRS is a cyclic quadrilateral. If $PS\left|\right|RQ$, then find the measure of $\angle PQR$.

Given: $\angle R={80}^o$

We know that the sum of either pair of opposite angles of a cyclic quadrilateral is 180^o.

So in cyclic quadrilateral PQRS,

$\angle P+\angle R={180}^o$

$\Rightarrow \angle P+{80}^o={180}^o$

$\Rightarrow \angle P={100}^o$

$\because PS\parallel RQ$

$\therefore \angle SPQ+\angle PQR={180}^o$

[The same-side interior angles sum up to 180^o.]

$\Rightarrow {100}^o+\angle PQR={180}^o$ [$\because \angle SPQ=\angle P={100}^o$]

$\Rightarrow \angle PQR={80}^o$

Hence, the measure of $\angle PQR={\mathbf{80}}^{\mathbf{o}}$