The moduli space of $n$-gons up to orientation preserving similarity can be identified with $\mathbb{C}P^{n-2}$, so I would say $2n-3$.

See On the moduli space of polygons in the Euclidean plane by Kapovich and Millson for more about this space.

The moduli space of $n$-gons up to orientation preserving similarity can be identified with $\mathbb{C}P^{n-2}$, so I would say $2n-3$.

See On the moduli space of polygons in the Euclidean plane by Kapovich and Millson for more about this space.

The moduli space of $n$-gons can be identified with $\mathbb{C}P^{n-2}$, so I would say $2n-4$.

See On the moduli space of polygons in the Euclidean plane by Kapovich and Millson for more about this space.

The moduli space of $n$-gons up to orientation preserving similarity can be identified with $\mathbb{C}P^{n-2}$, so I would say $2n-3$.

See On the moduli space of polygons in the Euclidean plane by Kapovich and Millson for more about this space.