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