The ratio of two complementary angles is 17:13. What is the measure of the smaller angle?

Let a be the smallest one

and then b be the bigger angle

we know that a+b = 90

we also given b/a=17/13

solve for a (smaller one)

b=90-a

replace b in the second equation by 90-a

we get (90-a) / a = 17/13

cross multiply

13 (90-a) = 17a

1170-13a=17a

1170=30a

1170/30=a

39=a

smallest angle is 39 degrees