Find the measure of two complementary angles, a and b, if m a = 7x + 4 and m b = 4x + 9

A would be 53 and b would be 37.

37 + 53 = 90 complementary angle = 90°

Complentary angles add to 90 degrees

a and b are complentary

a+b=90

a=7x+4

b=4x+9

so

7x+4+4x+9=90

combine like terms

11x+13=90

minus 13 both sides

11x=77

divide both sides by 11

x=7

m a = 7x+4=7 (7) + 4=49+4=53

m b=4x+9=4 (7) + 9=28+9=37

angle a measures 53 degrees

angle b measures 37 degrees