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

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

Given:
parallelogram ABCD,
angle B = 120 degrees,
BК – bisector of angle В,
AE = 6 centimeters,
DE = 2 centimeters.
Find the perimeter of a parallelogram ABCD -?
Solution:
1. Consider a parallelogram ABCD. Its opposite angles are equal to each other, then angle A = angle C, angle B = angle D = 120 degrees. The sum of the degree measures of the parallelogram is 360 degrees. Then:
angle A = angle C = (360 – 120 – 120): 2 = 120: 2 = 60 degrees. Side AD = 6 + 2 = 8 (centimeters).
2. Consider triangle ABE. Angle ABE = angle EBC = 60 degrees. Therefore, the ABE triangle is equilateral. Then AB = BE = AE = 6 centimeters.
3. Perimeter ABCD = 6 + 6 + 8 + 8 = 28 (centimeters).
Answer: 28 centimeters.




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