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,
[tex]m\angle A=95^\circ[/tex]
[tex]m\angle C=(4x-15)^\circ[/tex]
Since ABC is an isosceles triangle and AB=AC, therefore, the base angles are equal.
[tex]m\angle B=m\angle C=(4x-15)^\circ[/tex]
Using angle sum property of triangles, we get
[tex]m\angle A+m\angle B+\angle C=180^\circ[/tex]
[tex]95^\circ+(4x-15)^\circ+(4x-15)^\circ=180^\circ[/tex]
[tex](8x+65)^\circ=180^\circ[/tex]
[tex](8x+65)=180[/tex]
On further simplification, we get
[tex]8x=180-65[/tex]
[tex]8x=115[/tex]
[tex]x=\dfrac{115}{8}[/tex]
[tex]x=14.375[/tex]
Therefore, the value of x is 14.375.
