Let’s prove that the measurement of each angle of the equilateral triangle is 60°.

Given: an equilateral triangle

To prove the measurement of each angle of the equilateral triangle is 60°

Let ΔABC be an equilateral triangle,

We know all sides of the equilateral triangle are equal hence

Hence, AB = BC = AC

So we have to prove, ∠A = ∠B = ∠C = 60°

Now AB = AC

And we know angles opposite to equal sides are equal, so

⇒ ∠C = ∠B……..(i)

Also, AC = BC

And we know angles opposite to equal sides are equal, so

⇒ ∠B = ∠A……..(ii)

So from (i) and (ii), we get

∠A = ∠B = ∠C……….(iii)

Now in ΔABC,

We know in a triangle the sum of all three interior angles is equal to 180°.

So in this case,

∠A + ∠B + ∠C = 180°

Substituting value from equation (iii) in above equation we get

∠A + ∠A + ∠A = 180°

⇒ 3∠A = 180°

⇒ ∠A = 60°

Substituting this back in equation (iii), we get

∠A = ∠B = ∠C = 60°

Hence the measurement of each angle of the equilateral triangle is 60°

Hence proved