in an isosceles triangle the base angles are equal and the vertex angle is twice of each base angle . find the measures of the angles of the triangle..[linear equation]

Solution:

Let us assume that the base angle of the isosceles triangle be a^o, then the vertex angle will be 2a^o.

As we know that the sum of three angles of a triangle equal to 180^o.

a + a + 2a = 180

4a = 180

a = 180/4 = 45^o.

Since the base angles are equal, then the base angles are 45^o each, the vertex angle will be 2 x 45^o = 90^o.

Ans: Base angles: 45^o each Vertex angle: 90^o.