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##