Question

PQRS is a cyclic quadrilateral whose diagonals intersect at A. If $\angle SQR={80}^{\circ }$ and $\angle QPR={30}^{\circ },$ then find $\angle SRQ.$

• A. ${80}^{\circ }$
• B. ${60}^{\circ }$
• C. ${50}^{\circ }$
• D. ${70}^{\circ }$

Answer 1

The correct option is D ${70}^{\circ }$

Given, $\angle SQR={80}^{\circ }.$
Since angles in the same segment are equal, we have
$\angle SQR=\angle SPR={80}^{\circ }.$

But, $\angle SPQ=\angle SPR+\angle RPQ={80}^{\circ }+{30}^{\circ }$
$⟹\angle SPQ={110}^{\circ }$
Since opposite angles are supplementary in a cyclic quadrilateral, we have
$\angle SPQ+\angle SRQ={180}^{\circ }.$
$⟹\angle SRQ={180}^{\circ }–\angle SPQ={180}^{\circ }–{110}^{\circ }={70}^{\circ }$