Question

In fig., if $\angle ABC=20°$, then $\angle AOC$ is equal to

• A. $20°$
• B. $40°$
• C. $60°$
• D. $10°$

Answer 1

The correct option is B

$40°$

Use Subtended angle theorem

$\angle ABC=20°$

$\angle AOC=?$

The angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.

$\therefore \angle AOB=2\angle ABC$.

Now substitute the given value above we get.

$$\begin{gathered} \Rightarrow \angle AOB=2\angle ABC \\ \Rightarrow \angle AOB=2\times 20° \\ \Rightarrow \angle AOB=40° \end{gathered}$$

$\therefore \angle AOB$ is equal to $40°$.

Hence option B is correct.