Question

In the diagram, O is the centre of the circle. Find the value of $x$.

• A. ${111}^o$
• B. ${123}^o$
• C. ${69}^o$
• D. ${49}^o$

Answer 1

The correct option is A ${111}^o$

By using circle theorem which states that the measure of an angle subtended by an arc at the center is twice the measure of an angle subtended by the same arc at the circumference of the circle.

The exterior angle at the center is ${360}^o-{138}^o={222}^o$.

So, the value of $X$ is half of ${222}^o$ that is $\frac{{222}^o}{2}={111}^o$.

Hence, the answer is ${111}^o$.