Question

# Prove that the angles of an equilateral triangle are $$60^{\circ}$$ each.

Solution

## For an equilateral triangle, all sides are equal. Assuming an equilateral $$\Delta ABC,$$ Then, $$AB = AC = BC$$. $$\Rightarrow \angle A=\angle B= \angle C$$(Angles opp. to equal sides are equal)For a triangle, by angle sum property, $$\angle A+\angle B+\angle C= 180^{\circ}$$ Substituting $$\Rightarrow \angle A=\angle B= \angle C$$$$\therefore \angle A+\angle A+\angle A= 180^{\circ}$$$$\Rightarrow 3 \angle A= 180^{\circ}$$$$\Rightarrow \angle A= 60^{\circ}$$$$\therefore \angle A=\angle B=\angle C= 60^{\circ}$$So, each angle of an equilateral triangle is $$60º$$.MathematicsRS AgarwalStandard IX

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