Question

In an isosceles triangle , the base angles are equal, the vertex angle is twice

of either of the base angle. What are the degree measure of the angles of the

triangle​

Answer 1

Since the base angles of isosceles triangle are equal, therefore,

Let the base angles be 'x' and 'x'.

Also it is given that the vertex angle is twice its base angle, therefore,

Let the vertex angle be '2x'.

Using Angle Sum Property of Triangle,

x + x + 2x = 180°

4x = 180°

x = 180°/4

x = 45°

Now, base angles = x = 45°

& vertex angle = 2x = 90°.

Hence, it is a Right Angled Triangle

Answer 2

Given = Type of triangle = isosceles

Base angles are equal and vertex angle angle twice of either of base angle.

Find - Degree of measure of angle of given triangle.

Solution - Let the base angle of triangle be x.

Then, vertex angle = 2x

As we know, sum of all angles of triangle is 180°.

Thus, x + x + 2x = 180

4x = 180°

x = 180/4

x = 45°

Base angle = 45° and 45°

Vertex angle = 2x

Vertex angle = 2*45°

Vertex angle = 90°

Therefore, base angle is 45° each and vertex angle is 90°.