Question

Suppose ABC is an equilateral triangle. Its base BC is produced to D such that BC = CD. Calculate (i) ∠ACD and (ii) ∠ADC.

Answer 1

Given: AB = BC = CA

To Find: ACD and ADC

(i) AB = BC = CA (Given)

∠A = ∠B = ∠ACB (Angles opposite to equal sides are equal)

In ΔABC:

∠A + ∠B + ∠ACB = 180° (Sum of the angles of a triangle)

3∠ACB = 180°

∠ACB = 60°

(ii) In ΔACD:

AC = DC (Given)

∠CAD = ∠CDA (Angles opposite to equal sides are equal)

∠CAD + ∠CDA + ∠ACD = 180°

2∠CDA + 120° = 180°

2∠ADC = 60°

∠ADC = 30°