Question

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.

Answer 1

Let the base angles of the isosceles triangle be $x^{\circ }$ each.

According to the question,

The measure the vertex angle will be $(2x{)}^{\circ }$

we have,

$x+x+2x={180}^{\circ }$ (Sum of three sides of a triangle)

$\Rightarrow 4x^{\circ }={180}^{\circ }$

$\Rightarrow x^{\circ }=\frac{{180}^{\circ }}{4}$

$\Rightarrow x^{\circ }={45}^{\circ }$

$\Rightarrow x={45}^{\circ }$

Therefore, Each base angle measures are ${45}^{\circ }$

Vertex angle $=2\times {45}^{\circ }={90}^{\circ }$