Find the angles of a parallelogram a) one angle 52 b) the sum of two angles is 174 degrees c) one of the angles is 4

Find the angles of a parallelogram a) one angle 52 b) the sum of two angles is 174 degrees c) one of the angles is 4 times smaller than the other d) two angles are related as 4: 5

In solving the problem, we will use the theorem on the angles of a parallelogram: the sum of those adjacent to one side is 180 °, the opposite angles are equal. For convenience, let’s number the corners:
1, 3 and 2, 4 are opposite;
1,2 and 2, 3, etc. – adjacent to one side.

a) ∠ 1 = 52 °, adjacent to one side ∠ 2 = 180 ° – 52 ° = 128 °, ∠3 = ∠ 1 = 52 °, ∠ 4 = ∠ 2 = 128 °.
Answer: 52 °, 52 °, 128 °, 128 °.
b) The condition deals with opposite corners.
∠1 = ∠ 3 = 174 ° / 2 = 87 °.
∠4 = ∠2 = 180 ° – ∠1 = 180 ° – 87 ° = 93 °.
Answer: 87 °, 87 °, 93 °, 93 °.
c) The condition deals with the corners adjacent to one side.
∠ 1 = x, then ∠ 2 = 4x.
x + 4x = 180 °
5x = 180 °
x = 36 °:
4 * 36 = 144 °.
Answer: 36 °, 36 °, 144 °, 144 °.
d) We are talking about the corners adjacent to one side.
We introduce the coefficient of proportionality x and we get:
4x + 5x = 180 °
9x = 180 °
x = 20 °
4 * 20 = 80 °;
5 * 20 = 100 °.
Answer: 80 °, 80 °, 100 °, 100 °.