One of the angles of a parallelogram has a value 5 times the value of its other angle.

One of the angles of a parallelogram has a value 5 times the value of its other angle. Find the values of the remaining angles of the parallelogram.

Given:

ABCE – parallelogram,

angle A = 5 * angle B.

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 B be equal to x degrees, then the degree measure of angle A is 5 * x degrees. We know that the sum of the degree measures of a parallelogram is 360 degrees. Let’s make the equation:

x + x + 5 * x + 5 * x = 360;

x * (1 + 1 + 5 + 5) = 360;

x * 12 = 360;

x = 360: 12;

x = 30 degrees – the degree measure of the angle B;

30 * 5 = 150 degrees – the degree measure of angle A.

Answer: 150 degrees; 30 degrees; 150 degrees; 30 degrees.