The measure of the vertex angle of an isosceles triangle is 70. find the measure of a base angle of the triangle

Since the triangle is isosceles there are two congruent base angles and 1 vertex angle. The three angles add up to 180 degrees.
180 minus the vertex angle of 70 degrees leaves 110 degrees for the remaining two angles. Divide 110 by 2 to get the measure of each base angle.
180 - 70 = 110/2 = 55 degrees