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In an isosceles triangle, the two base angles are equal. The sum of all angles in a triangle is always 180 degrees.
Given that the vertex angle is 28 degrees, we can calculate the base angles as follows:
1. Subtract the vertex angle from 180 degrees:
\[
180^\circ - 28^\circ = 152^\circ
\]
2. Since the two base angles are equal, divide the remaining angle (152 degrees) by 2:
\[
\frac{152^\circ}{2} = 76^\circ
\]
Thus, each of the base angles measures **76 degrees**.