In trapezoid ABCD, point E is the middle of the large base AD, ED = BC, Angle B is 120 degrees Find the angle AEC and BCE.

By condition, ED = BC, and point E is the middle of the base AD, which means AE = ED = BC.
Consider a quadrilateral ABCE, in which BC = AE and they are parallel, hence ABCE is a parallelogram.
Angle ABC = 120, therefore, angle AEC = 1200 as the opposite angle of the parallelogram, angles BAE and ВСЕ are also equal as opposed.
The sum of the inner angles of the parallelogram is 3600. Then the angle BCE = (360 – 120 -120) / 2
120/2 = 60.
Answer: Angle AEC = 120, ВСЕ = 60.