Question

Please help and show workings

Answer 1

Given:

In an isosceles triangle,

One base angle = (4x-15)°

Vertex angle = 95°

To find:

The value of x.

Solution:

Let the triangle be ABC.

We have,

`m\angle A=95^\circ`

`m\angle C=(4x-15)^\circ`

Since ABC is an isosceles triangle and AB=AC, therefore, the base angles are equal.

`m\angle B=m\angle C=(4x-15)^\circ`

Using angle sum property of triangles, we get

`m\angle A+m\angle B+\angle C=180^\circ`

`95^\circ+(4x-15)^\circ+(4x-15)^\circ=180^\circ`

`(8x+65)^\circ=180^\circ`

`(8x+65)=180`

On further simplification, we get

`8x=180-65`

`8x=115`

`x=(115)/(8)`

`x=14.375`

Therefore, the value of x is 14.375.