The measures of two complementary angles are 6y+3 and 4y-13. Find the measures of the angles.

63° and 27°

2 complementary angles sum to 90°, hence

6y + 3 + 4y - 13 = 90

10y - 10 = 90 (add 10 to both sides)

10y = 100 (divide both sides by 10)

y = 10

The angles are

6y + 3 = (6 * 10) + 3 = 60 + 3 = 63°

4y - 13 = (4 * 10) - 13 = 40 - 13 = 27°

note that 63° + 27° = 90°

Y = 10 degrees

work:

6y + 3 + 4y - 13 = 90

6y + 4y = 90 + 13 - 3

10y = 100

y = 10