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.