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.
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