Mathematics
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.
Answer
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°.