One of the adjacent angles is 32 degrees larger than the other. Find the larger of these angles.

In order to find the larger of the angles given in the condition, we will compose and solve the equation.

It is known from the condition that one of the adjacent angles is 32 ° larger than the other.

Let’s remember that the sum of adjacent angles is 180 °.

We denote by x ° the smaller of the adjacent angles, then the larger of the adjacent angles is (x + 32) °.

We get the equation:

x + (x + 32) = 180;

We solve the equation:

x + x + 32 = 180;

2x = 180 – 32;

2x = 148;

x = 74 °.

The second adjacent angle is 74 + 32 = 106 °.

Answer: 74 ° smaller angle and 106 ° larger.