Prove that each angle of an equilateral triangle is 60°.

1.	Prove that each angle of an equilateral triangle is 60°.
Answer» Given to prove that each angle of the equilateral triangle is 60° Let us consider an equilateral triangle ABC Such that, AB = BC = CA Now, AB = BC ∠A = ∠C [i] (Opposite angles to equal sides are equal) BC = AC ∠B = ∠A [ii] (Opposite angles to equal sides are equal) From [i] and [ii], we get ∠A = ∠B = ∠C [iii] We know that, Sum of all angles of triangles = 180° ∠A + ∠B + ∠C = 180° ∠A + ∠A + ∠A = 180° 3∠A = 180° ∠A = \(\frac{180}{3}\) = 60° Therefore, ∠A = ∠B = ∠C = 60° Hence, each angle of an equilateral triangle is 60°

Answer»

Given to prove that each angle of the equilateral triangle is 60°

Let us consider an equilateral triangle ABC

Such that,

AB = BC = CA

Now,

AB = BC

∠A = ∠C [i] (Opposite angles to equal sides are equal)

BC = AC

∠B = ∠A [ii] (Opposite angles to equal sides are equal)

From [i] and [ii], we get

∠A = ∠B = ∠C [iii]

We know that,

Sum of all angles of triangles = 180°

∠A + ∠B + ∠C = 180°

∠A + ∠A + ∠A = 180°

3∠A = 180°

∠A = \(\frac{180}{3}\)

= 60°

Therefore, ∠A = ∠B = ∠C = 60°

Hence, each angle of an equilateral triangle is 60°

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