Triangles ABC is equilateral and BC = CE, then angle AEC is:

1. 60°

2. 45°

3. 30°

4. 120°

Since, ABC is an equilateral triangle, ∠A = ∠B = ∠C = 60°.

From figure,

⇒ ∠ACB + ∠ACE = 180° [Linear pairs]

⇒ 60° + ∠ACE = 180°

⇒ ∠ACE = 120°.

From figure, BC = CE (Given) ………………..(1)

⇒ BC = AC (Side of equilateral triangle) ……………….(2)

⇒ AC = CE (From equation (1) and (2))

⇒ ∠AEC = ∠CAE = y (let) [As angles opposite to equal sides of a triangle are equal]

By angle sum property in triangle AEC,

⇒ ∠AEC + ∠CAE + ∠ACE = 180°

⇒ y + y + 120° = 180°

⇒ 2y = 60°

⇒ y = 30°.

∴ ∠AEC = 30°.

Hence, option 3 is the correct option.