Question

In the adjoining figure, if $\angle QPR={60}^{\circ }$ and $\angle SPR={70}^{\circ }$, then $\angle QRS$= ___.

Answer 1

Clearly, QPSR is a cyclic quadrilateral.
In a cyclic quadrilateral, opposite angles are supplementary.
$⟹\angle QRS+\angle QPS={180}^{\circ }$
But, $\angle QPS=\angle QPR+\angle SPR={60}^{\circ }+{70}^{\circ }={130}^{\circ }$
$\therefore \angle QRS={180}^{\circ }-\angle QPS={180}^{\circ }-{130}^{\circ }={50}^{\circ }$