Question

In the given figure, if $\angle \text{OAB}={30}^{\circ }$, then $\angle \text{ACB}$ = ___.

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

Answer 1

The correct option is B ${60}^{\circ }$

Note that OA = OB = radius of the circle.

Since angles opposite to equal sides are equal, $\angle OAB=\angle OBA={30}^{\circ }.$

Using angle sum property in $△OAB,$ we have
$\angle AOB={180}^{\circ }-({30}^{\circ }+{30}^{\circ })={120}^{\circ }.$

Since the angle subtended by an arc at the centre is double the angle subtended by it at any remaining part of the circle, we have

$\angle ACB=\frac{\angle AOB}{2}={60}^{\circ }.$