In an isosceles trapezoid ABCD, the obtuse angle at the base is 130. Find the angle AQD

In an isosceles trapezoid ABCD, the obtuse angle at the base is 130. Find the angle AQD formed by the bisectors of the acute angles A and D.

Since the trapezoid, by condition, is isosceles, then its points at the base are equal to each other. ABC = BCD = 130, BAD = CDA.

The sum of the angles of the trapezoid is 360, then the angle BAD = CDA = (360 – 130 – 130) / 2 = 50.

Since DM and AH are the bisectors of the angles, the angle НD = MDA = 50/2 = 25.

Then the angle AQD = 180 – 25 – 25 = 130.

Answer: Angle АQD = 130.