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

40 degrees
Since the two angles are compliments they must add up to 90.
Call the angles ##x## and ##y##
Then
##x+ y = 90##
Since the angles are in ratio 4:5 we know that
##x = 4t## and ##y = 5t## where ##t## is there commonality.
so…
##x+ y = 90##
##4t + 5t = 90##
##9t = 90##
##t = 10##
##x = 4t##
##x = 4(10)##
##x = 40##