(i)

ABC is equilateral triangle.

∴ ∠ABC = ∠ACB = ∠BAC = 60°____________________ (i)

∠BDC = ∠BAC = 60°[Angles in the same segment of a circle are equal]

(ii)

ABCD is a cyclic quadrilateral

∴ ∠BAC + ∠BEC = 180°

⇒ 60° + ∠BEC = 180°

⇒ ∠BEC = 120°