Two angles are complementary. angle 1 is 15 degrees more than angle 2. what is the measure of angle 2?

∠2 = 37.5°

You have two relationships:

... ∠1 - ∠2 = 15°

... ∠1 + ∠2 = 90°

Subtracting the first equation from the second gives ...

... (∠1 + ∠2) -(∠1 -∠2) = (90°) -(15°)

... 2·∠2 = 75° . . . . simplify

... ∠2 = 37.5° . . . . . . divide by 2

Angle 1 and Check

The complement of angle 2 is ...

... ∠1 = 90° -37.5° = 52.5°

and the difference between the two angles is ...

... ∠1 - ∠2 = 52.5° -37.5° = 15° . . . . as required