In parallelogram ABCD BK is the bisector of angle ABC. Find the angles of the parallelogram if the angle ABK = 30 degrees.

Given:
parallelogram ABCD,
ВK – bisector of angle ABC,
angle AВK = 30 degrees.
Find the angles of the parallelogram ABCD: angle A, angle B, angle C, angle D -?
Decision:
1. Consider a parallelogram ABCD. Its opposite angles are equal to each other, then angle A = angle C, angle B = angle D. Since ВK is the bisector of angle ABC, then angle ABK = KBC = 30 degrees. Then the angle B = 30 * 2 = 60 degrees.
2. We know that the sum of the degree measures of the parallelogram is 360 degrees.
Then:
angle B = angle D = (360 – 60 – 60): 2;
angle B = angle D = 240: 2;
angle B = angle D = 120 degrees.
Answer: 120 degrees.