A trapezoid is a quadrilateral with four angles and the sum of the four angles is 360 degrees.
Britton rotated the trapezoid ABCD 180º, but we were not told that he tampered with the angles size or shape, we can now agree that it is still the same trapezoid that was rotated without any alterations in angles, size and shape.
Since we've been given that the angle B is 20º, and the measurement was not altered when rotating the trapezoid. Therefore the angle B' will also be 20º.