How to construct an n-gon by ruler and compass? Since $\cos[\frac{2\pi}{15}] $ is algebraic and equal to  $\frac{1}{8}(1+\sqrt{5}+\sqrt{30-6\sqrt{5}})$ we know that the regular 15-gon is constructible by ruler and compass.
Although I know how to construct a hexagon by ruler and compass and have seen the construction of a pentagon done in a youtube video, I can't find a description of a general approach to constructing n-gons where $n>7$ anywhere.
Is there a general approach, geometric algorithm if you like, to constructing an n-gon by ruler and compass?

In order to construct an angle equal to $\frac{2\pi}{15}$, you just need to construct an equilateral triangle and a regular pentagon, since:
$$ \frac{2\pi}{15} =\frac{1}{2}\left(\frac{2\pi}{3}-\frac{2\pi}{5}\right).$$
Have a look at the Wikipedia page about contructible regular polygons.
