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

$8x=180-65$

$8x=115$

$x=\dfrac{115}{8}$

$x=14.375$

Therefore, the value of x is 14.375.