Question

In the given figure, $O$ is the centre of the circle, Reflex $\angle AOB={260}^{\circ }$. $C$ is a point on the minor arc $AB$ of the circle. Find $\angle ACB$.

• A. ${100}^{\circ }$
• B. ${150}^{\circ }$
• C. ${80}^{\circ }$
• D. ${130}^{\circ }$

Answer 1

Answer: (D)

${130}^{\circ }$

We know, the angle at the center of a circle is twice the angle at the circumference subtended by the same arc. Hence,

$\angle ACB=\frac{1}{2}\times reflex\left(\angle AOB\right)$

$=\frac{260}{2}$

$={130}^{\circ }$