Two complementary angles have the ratio of 4:5. What is the measure of the smaller angle?

4x + 5x = 90 ... because complementary angles summed together equal 90 degrees
9x = 90
x = 10

smaller angle = 4x = 4(10) = 40

and if you wanted to find out the larger angle = 5x 5(10) = 50

and to check that they are complementary, 40 + 50 = 90