Please help and show workings

Question

asked May 6, 2022 158k views

1 Answer

Stinepike · Answer 1 · 2022-05-11T21:27:38+0000

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.