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Ne4ueva [31]
3 years ago
14

Please help and show workings

Mathematics
1 answer:
Scorpion4ik [409]3 years ago
8 0

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.

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