Question

Prove that each angle of an equilateral triangle is 60o
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Answer 1

Answer:

Given : ABC is an equilateral triangle whose AB=BC=CA

To Prove : A=B=C=60°

Proof : In triangle ABC,

AB=BC=CA (given)

Therefore, A=B=C (since, angles opposite to equal sides are equal)

Now, A+B+C=180° ( since, sum of all angles of a triangle is 180°)

Therefore, A=B=C=180°/3

A= B=C=60°

Hence, PROVED

Answer 2

By angle sum property we know that the sum of all the angles of a triangle is 180

We know that all the sides of a triangle are equal.

i.e all the angles of an equilateral triangle are equal.

Let each angle be x.

x+x+x=180

60o

3x = 180

⇒x = 60

Hence the answer.