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°
