Final answer:
The measure of the smaller angle is 55 degrees.
Step-by-step explanation:
To find the measure of the smaller angle, we need to understand what the complement of an angle is. The complement of an angle is the angle that, when added to the given angle, equals 90 degrees. Let's denote the measure of the angle as x degrees. According to the given information, the measure of the angle is 20 degrees more than its complement. So, we can set up the equation x = (90 - x) + 20.
Simplifying the equation, we get 2x = 110.
Dividing both sides by 2, we find that x = 55.
Therefore, the measure of the smaller angle is 55 degrees.