Find a measure of adjacent angles, one of which is 56 degrees larger than the other.

From the condition it is known that we are given two adjacent angles, one of which is 56 ° larger than the other. And we need to find the degree measure of these angles.

We start by recalling the sum of adjacent angles theorem. It says that the sum of adjacent angles is 180 °.

We denote by x ° the degree measure of the smaller angle, then the degree measure of the larger adjacent angle is (x + 56) °.

Let’s make the equation:

x + (x + 56) = 180;

x + x + 56 = 180;

2x = 180 – 56;

2x = 124;

x = 124: 2;

x = 62 ° smaller adjacent angle and (62 + 56) ° = 116 ° larger.