Question

In the given figure, what is the value of x?

• A. ${20}^{\circ }$
• B. ${10}^{\circ }$
• C. ${30}^{\circ }$
• D. ${15}^{\circ }$

Answer 1

The correct option is C ${30}^{\circ }$

Note that $\angle AOC+\angle COB={180}^{\circ }\left(\text{Linear pair}\right)$

$⟹\angle AOC={180}^{\circ }-\angle COB$
$={180}^{\circ }-{120}^{\circ }={60}^{\circ }$
Since an angle subtended by an arc at the centre of the circle is twice the angle subtended by it at any other point on the circle, we have
$x=\frac{1}{2}\angle AOC=\frac{1}{2}\times {60}^{\circ }={30}^{\circ }.$