In trapezoid ABCD, sides AB and CD are equal. The bisector of an obtuse angle B

| July 23, 2021 | education

In trapezoid ABCD, sides AB and CD are equal. The bisector of an obtuse angle B is perpendicular to the diagonal AC and cuts off the parallelogram FBCD from this trapezoid. Find the angle BCD

Since the sides of the trapezoid are equal, AB = CD, the trapezoid is isosceles, which means that the angles BAD and CDA are equal.

Since, by condition, BCDF is a parallelogram, then the angle FDC = FBC, as the opposite angle of the parallelogram.

The segment BF is the bisector of the angle ABC, then the angle ABF = FBC.

As a result, it turns out that in triangle ABF all angles are equal, and this is possible if triangle ABF is equilateral and its angles are 60.

Then the angle BAF = BAD = 60, then the opposite angle of the trapezoid is BCD = 180 – BAD = 180 – 60 = 120.

Answer: Angle ВСD = 120.



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