Find the value of the adjacent angle if one of them is 4 times larger than the other.

We are given two adjacent corners. It is known from the condition that one of them is 4 times larger than the other. And we need to find the degree measure of these angles.

For this we apply the theorem on the sum of adjacent angles. So, the sum of adjacent angles is 180 °.

Let’s compose and solve a linear equation.

Let’s denote by x ° the smaller of the adjacent angles, then the larger of the angles can be written as 4x °.

We get a linear equation:

x + 4x = 180;

5x = 180;

x = 180: 5;

x = 36 ° is the smaller angle, then 36 ° * 4 = 144 ° is the larger of the adjacent angles.

Answer: 36 ° and 144 °.