One of the angles of a parallelogram is four times the other angle of this parallelogram.

One of the angles of a parallelogram is four times the other angle of this parallelogram. Find the degree measures of the angles of this parallelogram

A parallelogram is a quadrilateral in which opposite angles are equal.

The sum of the degree measures of all the angles of the parallelogram is 360 °, the sum of the values of the angles of the parallelogram adjacent to one side is 180 °.

Since the angle ∠A is four times larger than the angle ∠B, we express these values as follows:

x is the value of ∠В;

4x – ∠A value;

x + 4x = 180;

5x = 180;

x = 180/5 = 36;

∠В = 36º;

∠А = 4 ∙ 36 = 144º.

Answer: the angles of the parallelogram are 36º, 144º.