Question

In the given figure, AB is the diameter of the circle and $\angle CBA={50}^{\circ }$, then the measure of $\angle CDB$ is equal to

• A.
  ${30}^{\circ }$
• B.
  ${60}^{\circ }$
• C.
  ${40}^{\circ }$
• D.
  ${50}^{\circ }$

Answer 1

The correct option is C

${40}^{\circ }$
We know that angles subtended by a chord in the same segment are equal.

$\therefore \angle ADC=\angle ABCNow,\angle ABC={50}^{\circ }\left(Given\right)\Rightarrow \angle ADC={50}^{\circ }Also,\angle ADB={90}^{\circ }(\therefore \text{Angle in a semicircle is a right angle})\therefore \angle CDB=\angle ADB–\angle ADC={90}^{\circ }–{50}^{\circ }={40}^{\circ }$

Hence, the correct answer is option (c).