Since the sum of complementary angles is 90 degrees, the measure of angle C added to the measure of angle D is equal to 90 degrees:

mC + mD = 90

But we know that the measure of angle D is 15 degrees less than that of angle C:

mD = mC + 15

Then, if you substitute mC = 15 in for mD in the first equation, you get:

mC + mC + 15 = 90

or 2mC + 15 = 90

subtract 15 from both sides: 2mC = 75

divide both sides by 2: mC = 37.5

The measure of angle C is 37.5 degrees.

Then to solve for mD plug back into the first equation:

mC + mD = 90

or 37.5 + mD = 90

subtract 37.5 from both sides: mD= 52.5

The measure of angle D is 52.5 degrees.

C + D = 90 (since they are complementary)

D = 2C - 15 - equation (2)

Substitute D from equation (2) into equation 1 to get:

C + 2C - 15 = 90

3C = 105

C = 35

D = 90 - 35 = 55