Question

In the figure, it is given that O is the centre of the circle and $\angle AOC={150}^{\circ }$. Find $\angle ABC$.

Answer 1

In circle with centre O and $\angle AOC={150}^{\circ }$

But $\angle AOC+reflex\angle AOC={360}^{\circ }$

$\therefore {150}^{\circ }+reflex\angle AOC={360}^{\circ }$

$\Rightarrow \angle AOC={360}^{\circ }-{150}^{\circ }={210}^{\circ }$

Now are AEC subtends $\angle AOC$ at the centre and $\angle ABC$ at the remaining part of the circle.

Reflex $\angle AOC=2\angle ABC$

$\Rightarrow {210}^{\circ }=2\angle ABC$

$\therefore \angle ABC=\frac{{210}^{\circ }}{2}={105}^{\circ }$