Find the angles of a parallelogram if one angle is 34 degrees greater than the other.

Given:
ABCE – parallelogram,
angle A = angle B + 34 degrees.
Find the degree measures of the angles of the parallelogram ABCE: angle A, angle B, angle C, angle E -?
Decision:
Consider a parallelogram ABCE. Its opposite angles are equal to each other, then angle A = angle C, angle B = angle E.
Let the degree measure of angle B be equal to x degrees, then the degree measure of angle A is equal to (x + 34) degrees. We know that the sum of the degree measures of a parallelogram is 360 degrees. Let’s make the equation:
x + x + x + 34 + x + 34 = 360;
x + x + x + x + 68 = 360;
x + x + x + x = 360 – 68;
x + x + x + x = 292;
x * (1 + 1 + 1 + 1) = 292;
x * 4 = 292;
x = 292: 4;
x = 73 degrees – the degree measure of the angle B;
73 + 34 = 107 degrees is the degree measure of angle A.
Answer: 107 degrees; 73 degrees; 107 degrees; 73 degrees.