Question:
Prove that each angle of an equilateral triangle is 60°.
Solution:
Given to prove each angle of an 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]
And BC = AC
∠B = ∠A ... (ii)
From (i) and (ii), we get
∠A = ∠B = ∠C ... (iii)
We know that
Sum of angles in a triangle = 180
∠A + ∠B + ∠C = 180
∠A + ∠A + ∠A = 180
3∠A = 180
∠A = 60
∠A = ∠B = ∠C = 60
Hence, each angle of an equilateral triangle is 60°.
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