Question

In the following figure, $O$ is centre of the circle and $\Delta ABC$ is equilateral.
Find :
(i) $\angle ADB$
(ii) $\angle AEB$

Answer 1

REF.Image.

we know that angle subtended by a chord

(i) is same when both are on same side of arc/ chord

(ii) sum = ${180}^{\circ }$ when both are on

opposite sides

Given $\angle ACB={60}^{\circ }$ (equilateral)

$\therefore \angle ADB={60}^{\circ }$ [same side of chord]

$\angle ACB+\angle AEB={180}^{\circ }$

$\Rightarrow \angle AEB=180-60={120}^{\circ }$ [opposite side]