Question

If the measure of the exterior angle adjacent to the vertex angle of an isosceles triangle is 105 degrees find the measure of the base angle

Answer 1

Given:

The measure of the exterior angle adjacent to the vertex angle of an isosceles triangle is 105 degrees.

To find:

The measure of the base angle.

Solution:

We know that the base angles of an isosceles triangle are equal.

Exterior angle theorem: In a triangle, the sum of two interior angles of the triangle is equal to the opposite exterior angle.

Let x be the measure of the base angle. Then the other base angle is also x.

Sum of base angles = x + x

                                 = 2x

Using exterior angle theorem,

Sum of base angles = Measure of the exterior angle adjacent to the vertex

$2x=105^\circ$

$x=\dfrac{105^\circ}{2}$

$x=52.5^\circ$

Therefore, the measure of the base angle is equal to 52.5 degrees.