Question

In an isosceles triangle if the vertex angle is twice the sum of the base angle calculate the angles of the triangles.

Answer 1

2(x+x)+x+x=180
4x+x+x=180
6x=180
x=180/6=30

base angles=30
vertex angle=2(30+30)=2x60=120

Answer 2

let the 1st base angle be x                    (equation 1)
the 2nd base angle be y=x (beacuase it is an isosceles triangle)       (equation 2)
so according to the question,2(x+x)=vertex angle  ⇒2(2x)=4x=vertex angle                 (equation 3)
adding equations 1,2 and 3 we have,
x+x+4x=180°            (angle sum property of a triangle)
⇒6x=180°
⇒x=180°÷6
∴x=30°

∴the angles of the triangle are:
vertex angle=4x=4×30°=120°
base angles=x=30°


hope it helps you :)