Let x be the measure of the larger angle. Then, the smaller angle is x - 22 degrees. Since the angles are complementary, we know that their sum is 90 degrees. So, we can write an equation:
x + (x - 22) = 90
Simplifying this equation, we get:
2x - 22 = 90
Adding 22 to both sides, we get:
2x = 112
Dividing both sides by 2, we get:
x = 56
Therefore, the larger angle is 56 degrees, and the smaller angle is:
x - 22 = 56 - 22 = 34 degrees.
So, the measure of the smaller angle is 34 degrees.