One of two supplementary angles is five times the other. find the angles. (recall that supplementary angles are angles whose sum is 180 degrees.) which equation can be used to solve for the smallest angle?

The angles are 30 degrees and 150 degrees.  You can write 2 equations with 2 variables.  Let s = the smaller angle, and g = the larger angle.  
s + g = 180
5s = g
You can substitute 5s in for g in the first equation.
s + 5s = 180
6s = 180
s = 30
Plug 30 in for s in the equation s + g = 180.
30 + g = 180
g = 150