Please relocate if this isn't the proper forum.

I teach a high school math course and we have been working on fermat primes, unmarked straightedge and compass constructions,and so on. We've trisected given angles with a marked straightedge, enabling us to construct regular 7-gons and 9-gons. Now we are wondering if we can "quinsect" a given angle with a marked starightedge and compass. Answers, hints, and indications in the right direction are welcome.
Thanks