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.

Answer 1

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}.