In an isosceles triangle, the two base angles are equal. To find the measure of the base angles when you know the vertex angle, you can use the fact that the sum of all angles in a triangle is always 180 degrees.
Given that the vertex angle is 84 degrees, we can first subtract this angle from 180 degrees:
180 degrees – 84 degrees = 96 degrees.
This is the total measure of the two base angles combined. Since both base angles are equal, we divide this result by 2:
96 degrees ÷ 2 = 48 degrees.
Therefore, each base angle measures 48 degrees.