In an isosceles triangle, the base angles are congruent (have the same measure) and the vertex angle is opposite the base. Since one of the base angles measures 16 degrees, the other base angle also measures 16 degrees. Therefore, the sum of the base angles is 16 + 16 = 32 degrees.
Since the sum of the angles in any triangle is 180 degrees, we can find the measure of the vertex angle by subtracting the sum of the base angles from 180 degrees.
So, the measure of the vertex angle of the isosceles triangle is:
180 - 32 = 148 degrees.