# In isosceles trapezoid ABCD with base AD and BC, heights BH and CM are drawn, angle BAH = 57 degrees. find the DCM angle.

August 24, 2021 | education

| Since the trapezium ABCD is isosceles, the angles at its base are equal, hence the angle BAD = CDA = 57.

The first way.

Consider a triangle CMD. Since the CM is the height to the base of the CM by condition, the angle CMD = 90. Then the sought angle is DCM = 180 – 90 – 57 = 33.

Second way.

Determine the obtuse angles of the trapezoid at the base of the BC. (360 – 2 * 57) / 2 = 246/2 = 123.

Then the angle СМD = ВСD – 90 = 123 – 90 = 33.

Answer: Angle CMD = 33.

One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.