Question

In the given figure, O is the centre of the circle. If $\angle PQR={130}^{\circ }$ , then the measure of $\angle RPT$ is

• A.
  ${50}^{\circ }$
• B.
  ${30}^{\circ }$
• C.
  ${45}^{\circ }$
• D.
  ${40}^{\circ }$

Answer 1

The correct option is D

${40}^{\circ }$
Given: $\angle PQR={130}^{\circ }Also,\angle PQT={90}^{\circ }(\because \text{Angle in a semicircle is a right angle})\therefore \angle RQT=\angle PQR–\angle PQT={130}^{\circ }–{90}^{\circ }={40}^{\circ }Now,\angle RPT=\angle RQT(\because \text{Angles in the same segment are equal})\therefore \angle RPT={40}^{\circ }\text{Thus, the measure of}\angle RPTis{40}^{\circ }.$

Hence, the correct answer is option (d).