A tiling is a decomposition of a polygon into finitely many non-overlapping triangles. We prove that if a regular n-gon, $n \geq 5$, $n \neq 28$, can be tiled with similar right triangles, then one of the angles of these triangles is in $\left\{\fracπ{n},\frac{2π}{n}, \fracπ {6}+\frac{2π}{3n}\right\}$. Some related results were previously obtained by M.Laczkovich and B. Szegedy.