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
