Find all the angles of a parallelogram if the sum of two of them is 100 degrees

Find all the angles of a parallelogram if the sum of two of them is 100 degrees.)

By the property of a parallelogram, the angles adjacent to one side are equal to 180, therefore the angle (A) in the sum of the angle (B) is 180 as well as the sum of the angles (C) and (D).

Angle (A) + angle (C) = 100 – by condition.

By the property of a parallelogram, its opposite angles and sides are equal, and therefore the angle (A) is equal to the angle (C). => angle (A) = angle (C) = 100/2 = 50.

Since angle (A) + angle (B) = 180, then angle (B) = 180 – angle (A) = 180 – 50 = 130, and angle (D) = angle (B) – by property, therefore the angle ( D) = 130.

Answer: angle (A) = 50, angle (B) = 130, angle (C) = 50, angle (D) = 130.