Question

prove that the angles of equilateral triangle measure 60 degree each​

Answer 1

Answer:

In an equilateral triangle, all the sides are equal.

Since angles opposite to equal sides are equal in a triangle, the three angles are equal.

By angle sum property of a triangle, Angle1 + Angle2 + Angle3 = 180.

Let one angle be X.

Then all angles = X.

Therefore,   X + X + X = 180.

3X = 180.

X = 60.

All angles are equal to 60.

Step-by-step explanation:

Answer 2

Solutions:

Let △ABC be an equilateral triangle. Then, AB = BC = CA.

Since, angles opposite to equal sides of a triangle are equal.

Hence, AB = BC and BC = CA

=> ∠C = ∠A and ∠A = ∠B

=> ∠A = ∠B = ∠C ............... (i)

Using angle sum property in△ABC, we obtain

∠A + ∠B + ∠C = 180°

=> ∠A + ∠A + ∠A = 180° .....[Using (i)]

=> 3∠A = 180°

=> ∠A = 60°

Hence, ∠A = ∠B = ∠C = 60°