The isosceles trapezoid is part of an isosceles triangle with a 38° vertex angle. What is the measure of an acute base angle of the trapezoid? The diagram is not drawn to scale.
Since the isosceles trapezoid is part of an isosceles triangle, the base angles of the trapezoid are congruent to the base angles of the triangle. Since the triangle has a 38° vertex angle, the sum of the base angles is 180° - 38° = 142°.
Since the trapezoid is isosceles, the base angles are congruent, so each base angle measures 142° ÷ 2 = <<142/2=71>>71°.
Therefore, the measure of an acute base angle of the trapezoid is 71°. Answer: \boxed{71}.