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 1800, therefore the angle (A) in the sum of the angle (B) is 1800 as well as the sum of the angles (C) and (D). Angle (A) + angle (C) = 1000 – 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) = 1000/2 = 500. Since angle (A) + angle (B) = 1800, then angle (B) = 1800 – angle (A) = 1800 – 500 = 1300, and angle (D) = angle (B) – by property, hence the angle ( D) = 1300. Answer: angle (A) = 500, angle (B) = 1300, angle (C) = 500, angle (D) = 1300. 2) Find all the angles of the parallelogram if the difference between two of them is 70 degrees. By the property of the parallelogram, the angle (A) + (B) = 1800. We make up the system: angle (A) + angle (B) = 1800, angle (A) – angle (B) = 700. Subtract the bottom line from the top line and get 2 angles (A) = 1100, angle (A) = 1100/2 = 550, therefore the angle (B) = 1800 – 550 = 1250. By the property of a parallelogram, angle (A) = angle (C) = 550, angle (D) = angle (B) = 1250.
Answer: angle (A) = 550, angle (B) = 1250, angle (C) = 550, angle (D) = 1250.