why the sum of three sides of a triangle is 180 degree?
Let us see about the angle sum property of the triangle.
Here the base of the triangle has been extended and we get an exterior angle d which is adjacent to the interior angle c. As the sum of an interior angle and its adjacent exterior angle is 180º, c + d = 180º.
The exterior angle of a triangle is equal to the sum of the two opposite interior angles.
Thus, We get c + d = 180º
c + a + b = 180º
a + b + c = 180º.
So the sum of three angles of a triangle is 180º. In any triangle ABC, the sum of the three triangles which can be given as
∠A + ∠B +∠C = 180º.