In the figure (1) given below, ABC is an equilateral triangle. Base BC is produced to E, such that BC = CE. Calculate ∠ACE and ∠AEC.

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

From figure,

∠ACB + ∠ACE = 180°

60° + ∠ACE = 180°

∠ACE = 120°.

From figure,

∠AEC = ∠CAE (As angles opposite to equal sides are equal)

Let ∠AEC = ∠CAE = y.

From figure,

∠AEC + ∠CAE + ∠ACE = 180°

y + y + 120° = 180°

2y = 60°

y = 30°.

Hence, ∠ACE = 120° and ∠AEC = 30°.