Find the measures of two adjacent angles if their difference is 30 degrees.

In order to find the degree measure of two adjacent angles, if it is known that the difference between these angles is 30 °.

To solve the problem, we will compose and solve the equations. And we will start with the introduction of the variable x ° the degree measure of the smaller angle, then (x + 30) ° the degree measure of the larger angle.

To compose the equation, we will use the triangle sum theorem. Which says that the sum of adjacent angles is 180 °.

x + (x + 30) = 180;

x + x + 30 = 180;

2x = 180 – 30;

2x = 150;

x = 75 ° smaller angle and (75 + 30) = 105 ° larger angle.