Question

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

Answer 1

Given to prove that 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            ................(1) [Opposite angles to equal sides are equal] 

and BC = AC ⇒∠B = ∠A ……..(2) 

From (1) and (2), we get 

∠A = ∠B = ∠C          ..............(3) 

We know that
Sum of angles in a triangle =180° 

⇒∠A+∠B+∠C=180° 

⇒ ∠A+∠A+∠A=180° 

⇒3 ∠A=180°  

⇒ `∠A=(180°)/3=60°` 

∴∠S=∠B=∠C=60° 

Hence, each angle of an equilateral triangle is 60°.