In parallelogram ABCD, the bisectors BE and CE of angles B and C intersect at point E

| May 27, 2021 | education

In parallelogram ABCD, the bisectors BE and CE of angles B and C intersect at point E, which lies on side AD. Find BE if angle BEC + angle ABE = 150 ° and BC = 12.

Since BE is the bisectors of the angle ABC, then the angle ABE = CBE, and then the sum of the angles CBE + BEC = 150.

Then in the triangle BCE the angle BCE = (180 – 150) = 30.

Since the CE is the bisector of the angle ВСD, the angle ВСD = 2 * ВСE = 2 * 30 = 60.

In a parallelogram, the sum of adjacent angles is 180, then the angle ABC = (180 – 60) = 120.

Since BE is the bisectors of the angle ABC, the angle CBE = 120/2 = 60.

In the triangle BCE, the angle CBE = 60, the angle BCE = 30, then the angle BEC = 180 – 60 – 30 = 90, which means that the triangle ALL is rectangular.

The leg BE lies against an angle of 30, then BE = BC / 2 = 12/2 = 6 cm.

Answer: The length of the bisector BE is 6 cm.



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