Age 14 to 16
If you have decided that the result holds for a regular hexagon, what is it exactly about the hexagon that lets it work?
What does a regular hexagon also have that isn't needed for this result?
For the regular pentagon, put a point somewhere inside, perhaps not at the centre.
Join that point to each of the vertices of the pentagon and think about the five triangles.
Finally, what does a regular pentagon also have that isn't needed for this result?