Question

In Fig 10.4 if $\angle ABC={20}^{\circ }$ then $\angle AOC$ is equal to

• A. ${20}^{\circ }$
• B. ${40}^{\circ }$
• C. ${60}^{\circ }$
• D. ${10}^{\circ }$

Answer 1

The correct option is B ${40}^{\circ }$

We know that the angle at the centre of the circle is twice the angle at the circumference subtended by the same arc.

Thus,

$\angle AOC=2\times \angle ABC$

$⟹\angle AOC=2\times {20}^0$

$⟹\angle AOC={40}^0$