In parallelogram ABCD, the angle B is equal to 120 degrees and the bisector of this angle divides the AD

| January 30, 2021 | education

In parallelogram ABCD, the angle B is equal to 120 degrees and the bisector of this angle divides the AD side into segments AE = 6cm and DE = 2cm. Find the angles of a parallelogram

Since AВСD is a parallelogram, the sum of its adjacent angles is 180.

Then the angle AВD = (180 – ABC) = 180 – 120 = 60.

The opposite angles of the parallelogram are equal, then the angle A = C = 600, the angle B = D = 120.

Answer: The angles of the parallelogram are 60 and 120.

By the property of the bisector of a parallelogram, it cuts off an isosceles triangle.

Then in the triangle ABE AB = AE = 6 cm.

Then AB = CD = 6 cm, AD = BC = AE + DE = 6 + 2 = 8 cm.

Ravsd = 2 * (AB + AD) = 2 * (6 + 8) = 2 * 14 = 28 cm.

Answer: The perimeter of the parallelogram is 28 cm.

Parallelogram has opposite sides parallel, then AD || BC, which means ED || BC, and then BCDE is a trapezoid.

Answer: BCDE is a trapezoid.



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