Question

In an isosceles triangle, the base angles are equal and the vertex angle is twice the base angle. find the measures of each angle. what type of triangle is it

Answer 1

in an isosceles triangle, the base angles are congruent 
if the base angle is x, the the vertex is 2x 
hence, x+x+2x=180 
let x= be the base angle 
2x = be the vertex 
x+x+2x=180 
4x=180 
x=45 
2x=90 
then vertex is 90 degrees

Answer 2

The angles are 45°,45°,90°.

The triangle is a right angled isosceles triangle.

Given data :

Vertex angle is twice than the each of the equal base angles.

Let,base angle = x

So,vertex angle = 2x

Total angle is always 180° of a triangle.

So,

x+x+2x = 180

4x = 180

x = 45

So,the two base angles are 45°. (Answer)

Vertex angle = 2×45° = 90.(Answer)

And,the triangle is a right angled isosceles triangle.