Question 62782
Consider an equilateral triangle,

all the sides are equal.

Let the all the sides of triangle = 1cm

And A be the angle of the first side,
B be the third angle for the second side.
c be the second angle for the third side
Now we know the sine rule,

SinA / first side = Sin B /second side = SinC /third side 

SinA /1 = sinB / 1 = Sin C/1

SinA =SinB =SinC

A =B=C
We know that the sum of the triangle is equal to 180 degree,

angleA+ angleB + angle C = 180

Since all the angles are same,

We write  the above equation as,

3angle A = 180

angle A =180 /3 = 60

Angle A =angleB=Anglec= 60

or measure of A = 60

   measure of B =60
   
   measure of c = 60