Hi Mitch—this is certainly beyond the scope of this course, but I'll respond here given that I know the answer.
Two things come to mind: the first is a bit trivial, but it works—simply multiply your result by {1,180 Degree/Pi. So for your code,
{1,180 Degree/Pi}*ToPolarCoordinates[FromPolarCoordinates[{5, 36.87 °}] + FromPolarCoordinates[{10, -53.13 °}]]
Alternatively, you could construct it like:
MapAt[180 Degree/Pi*#&,yourData,2]
This is nice in that it's extensible to a list of {r,theta} pairs just by doing:
MapAt[180 Degree/Pi*#&,yourData,{All,2}]
Hopefully that helps.