Question

In the adjoining figure, if $\angle QPR={67}^{\circ }$ and $\angle SPR={72}^{\circ }$, then $\angle QRS$ is equal to

• A. 41
• B. 23
• C. 67
• D. 18

Answer 1

The correct option is A

41

Clearly, it is a cyclic quadrilateral.
So, $\angle QRS={180}^{\circ }-\angle QPR-\angle SPR$ [Sum of opposite angles of a cyclic quadrilateral is ${180}^{\circ }$]

$\Rightarrow {180}^{\circ }-({67}^{\circ }+{72}^{\circ })={41}^{\circ }$

$\therefore \angle QRS={41}^{\circ }$