Question

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

• A. ${50}^{\circ }$
• B. ${70}^{\circ }$
• C. ${60}^{\circ }$
• D. ${65}^{\circ }$

Answer 1

The correct option is A

${50}^{\circ }$

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