The isosceles trapezoid is part of an isosceles triangle with a 38° vertex angle. What is the measure of an obtuse base angle of the trapezoid? The diagram is not drawn to scale.
Since the trapezoid is part of an isosceles triangle, the base angles of the trapezoid are equal in measure to the base angles of the isosceles triangle that are opposite the congruent sides. Since the vertex angle of the isosceles triangle is 38°, the base angles are equal in measure and each measures (180° - 38°)/2 = <<(180-38)/2=71>>71°. This means that an obtuse base angle of the trapezoid also measures $\boxed{71}$°.
