The isosceles trapezoid is part of a isosceles triangle with with a 32 degree vertex angle, what is the measure of an acute base angle of a trapezoid

Let be Δ ABC with DE, a parallel intercepting both side of this Isosceles Δ

<BAC =32°, so both angle of the base of this Δ = 180° - 32° = 148°
Since the angle at the base are equal then each angle of the triangle, as well as the trapezoid = 74°