ToT 2004-fall SA6

Let n be a fixed prime number >3. A triangle is said to be admissible if the measure of each of its angles is of the form $\frac{m\cdot 180^{\circ}}{n}$ for some positive integer m. We are given one admissible triangle. Every minute we cut one of the triangles we already have into two admissible triangles so that no two of the triangles we have after cutting are similar. After some time, it turns out that no more cuttings are possible. Prove that at this moment, the triangles we have contain all possible admissible triangles (we do not distinguish between triangles which have same sets of angles, i.e. similar triangles).