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

One corner of a parallelogram is four times the other angle of this parallelogram. Find the measure of the smaller of the angles of the parallelogram.

In order to find the angles of a parallelogram, we will compose and solve an equation.

Let’s look at what we know from the condition. The condition says that one corner of the parallelogram is 4 times larger than the other.

There are two kinds of angles in a parallelogram:

1. opposite – they are equal to each other;

2. one-sided – their sum is 180 °.

In our case, we are talking about one-sided. Let’s denote one of the corners as x, then 4x is the second corner.

x + 4x = 180;

x (1 + 4) = 180;

5x = 180;

x = 180: 5;

x = 36 ° smaller angle and 36 * 4 = 144 ° larger angle.