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

Δ ABC is an equilateral triangle

CD is drawn such that CD = BC

∠ACB = 60⁰(Interior angle of an equilateral triangle)

∠ACD = 180⁰-60⁰ = 120⁰(Angle on a straight line)

In an equilateral triangle since all sides are equal so

AC = CD

Hence Δ ACD is isosceles

Since base angles of an isosceles triangle is equal so

∠CAD = ∠CDA = x(Let us assume)

∠ACD + ∠CAD + ∠CDA = 180⁰(Sum of interior angles of a triangle)

⇒ 2x = 180⁰-120⁰ = 60⁰

⇒ x = 30⁰

∠ADC = 30⁰