Question

In the given figure, if $O$ is the centre of the circle, then find $x$.

• A. ${55}^o$
• B. ${208}^o$
• C. ${52}^o$
• D. None of these

Answer 1

Answer: (C)

${52}^o$

We know that the angle subtended at the centre of the circle by an arc is twice the angle subtended by the same arc at any point on the circumference of the circle.
$\angle AOB$ is the angle at the center and $\angle ACB$ is the angle at the circumference.
$\therefore \angle ACB=\frac{1}{2}\angle AOB=\frac{1}{2}\left({104}^o\right)={52}^o$