Question

In the figure, $\angle$CBD$={110}^o$. Find $\angle$AOC.

Answer 1

Given that:

$\angle CBD={110}^{\circ }$

To find:

$\angle AOC=?$

Solution:

$\angle ABC+\angle CBD={180}^{\circ }$ (Linear pair)

or, $\angle ABC+{110}^{\circ }={180}^{\circ }$

or, $\angle ABC={70}^{\circ }$

$\angle AOC=2\angle ABC$ (Angle subtended by an arc at the centre is twice of the angle subtended by it at any point on the circle.)

or, $\angle AOC=2\times {70}^{\circ }={140}^{\circ }$