A coprime pair of positive integers are two which have
no factors in common other than 1.

A composite integer has three or more factors.

We prime factor 80:

80 = 8*10 = 2*2*2*2*5

Pick an integer that has at least 3 factors, in order to
be composite, that doesn't have either 2 or 5 as a factor.
The smallest one we could pick would be 3*3 = 9, it has 
three factors 1,3,and 9. Or we could pick 3*7 or 21.  It
has 4 factors 1,3,7,and 21.  (80,9) is a coprime pair.
So is (80,27).
 
Edwin