Answer :
(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°
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