In the given figure, O is the centre of the circle and ΔABC is equilateral. Find :

(i) ∠BDC

(ii) ∠BEC.

(i) Since ABC is an equilateral triangle so,

∠A = ∠B = ∠C = 60°.

From figure,

∠BDC = ∠BAC (Angles in same segment are equal.)

∴ ∠BDC = 60°.

Hence, ∠BDC = 60°.

(ii) BDCE is a cyclic quadrilateral. Hence, sum of the opposite angles = 180°.

⇒ ∠BDC + ∠BEC = 180°

⇒ 60° + ∠BEC = 180°

⇒ ∠BEC = 180° - 60° = 120°.

Hence, ∠BEC = 120°.