Question

If $O$ is the centre of the circle, find $\angle ABC$ in the figure given below.

• A. ${31}^o$
• B. ${30}^o$
• C. ${62}^o$
• D. ${124}^o$

Answer 1

The correct option is A ${31}^o$

We know: The angle subtended by an arc at the center of the circle is double the angle subtended by the same arc at any point of rest part of circumference of the circle.

In the figure, minor arc $AC$ is subtending $\angle ABC$ at the circumference and $\angle AOC$ at the centre of the circle.

So, $\angle ABC=\frac{\angle AOC}{2}$
$\angle ABC=\frac{{62}^o}{2}$
$\angle ABC={31}^o$

So, option $\left(a\right)$ correct.