Find the angles of a parallelogram ABCD if the angles to one side of the parallelogram are 3: 6.

Given:
ABCE – parallelogram,
angle A: angle E = 3: 6.
Find the degree measures of the angles of the parallelogram ABCE: angle A, angle B, angle C, angle E -?
Solution:
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 A be 3 * x degrees, then the degree measure of angle E is 6 * x degrees. We know that the sum of the degree measures of a parallelogram is 360 degrees. Let’s make the equation:
3 * x + 3 * x + 6 * x + 6 * x = 360;
x * (3 + 3 + 6 + 6) = 360;
x * 18 = 360;
x = 360: 18;
x = 20 degrees;

20 * 3 = 60 degrees – the degree measure of the angle A;
20 * 6 = 120 degrees – the degree measure of the angle E.
Answer: 60 degrees; 120 degrees; 60 degrees; 120 degrees.