Angle a and Angle B are complementary. The measures of complementary angles have a sum of 90 degrees. The measures of the angles have a difference of 20 degrees. What are the measures of the angles?

As you said, complementary angles are angles which sum up to 90 degrees. We know that there are two angles (A and B), so we can divide 90 degrees into two equal parts:

90 : 2 = 45

Now we can add 10 and substract 10 from the result to get measures of both angles:

45 - 10 = 35

45 + 10 = 55

And these are the measures of both angles we're looking for - all conditions are met:

35 degrees + 55 degrees = 90 degrees (so they are complementary)

55 degrees - 35 degrees = 20 degrees (so there's a difference of 20 degrees between them)