Question

In the figure, PQ is the diameter of the semicircle in which $\angle SPR={30}^{\circ };\angle QPR={20}^{\circ }$ ;
then $\angle SRP$ equals :

• A. ${40}^{\circ }$
• B. ${65}^{\circ }$
• C. ${120}^{\circ }$
• D. ${35}^{\circ }$

Answer 1

The correct option is A ${40}^{\circ }$

$PQ$ is diameter so $\angle PSQ={90}^o$ (angle in a semi circle)

In $△PSQ$, $\angle SPQ=30+20={50}^o\Rightarrow \angle SQP={40}^o$

$\angle SQP=\angle SRP={40}^o$ as these angles are in the same segment.