Q. 44.0( 24 Votes )

# Suppose ABC is an

Answer :

Δ ABC is an equilateral triangle

CD is drawn such that CD = BC

∠ACB = 60^{0}(Interior angle of an equilateral triangle)

∠ACD = 180^{0}-60^{0} = 120^{0}(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 = 180^{0}(Sum of interior angles of a triangle)

⇒ 2x = 180^{0}-120^{0} = 60^{0}

⇒ x = 30^{0}

∠ADC = 30^{0}

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