Question

In the given figure, $O$ is the centre of the circle and $\angle A B C=60^{\circ}$ then the measure of $\angle C D B$ (in degrees) is ___

Answer 1

' $O^{\prime}$ is the centre of the circle with diameter $A B$.
$\angle A C B=90^{\circ}$
$\{\because$ Angle subtended on the area of the semicircle is $\left.90^{\circ}\right\}$
Given: $\angle A B C=60^{\circ}$
Now, in $\triangle A C B$
$ \angle A C B+\angle C A B+\angle C B A=180^{\circ} $
$\Rightarrow 90^{\circ}+\angle C A B+60^{\circ}=180^{\circ} $
$ \Rightarrow \angle C A B=180^{\circ}-150^{\circ}=30^{\circ}$
$ \angle C A B=\angle C D B=30^{\circ}$
$\{\because$ Angles in the same segment of a circle are equal.$\}$