Question

Solution of isosceles triangle if vertex angle is twice the sum of base angles .Calculate angle of triangle

Answer 1

let the each  base angles of isosceles triangle = x    

so sum  of two equal base angles = x + x = 2x

vertex angle = twice of sum  of two equal base angles = 2 × 2x = 4x

vertex angle = 4x

sum of the three angles = x + x + 4x = 6x

By angle sum property of triangle , sum of the three angles = 180°

⇒ 6x = 180°

⇒  x = 180/6 = 30°

and 4x = 4 × 30 = 120°

Hence three angles are of 30° , 30° and 120°.