Question

$A,B$ and $C$ are three points on a circle with centre $O$ such that $\angle BOC$ is equal to ${30}^{\circ }$ and $\angle AOB$ is equal to ${60}^{\circ }$. If $D$ is another point on the circle other than the arc $ABC$ find $\angle ADC$.

Answer 1

$\angle AOB={60}^{\circ }$

$\angle BOC={30}^{\circ }$

Here, $\angle AOC=\angle AOB+\angle BOC$

$\angle AOC={60}^{\circ }+{30}^{\circ }$

$\angle AOC={90}^{\circ }$

Since arc $ABC$ makes an angle of ${90}^{\circ }$ at the centre of the circle.

$\angle ADC=\frac{1}{2}\angle AOC$

$\angle ADC=\frac{1}{2}\left({90}^{\circ }\right)$

$\angle ADC={45}^{\circ }$

Hence, $\angle ADC={45}^{\circ }$