We present a new approach based on the Slope Chain Code to determine whether a curve is rotational symmetrical and its order of symmetry. The proposed approach works for open and closed perfectly symmetrical or quasi-symmetrical 2D curves. Simple operations on the SCC and its invariant properties are central to our methodology. To evaluate the proposed methodology, we use 1400 curves from a public database. For the symmetrical/asymmetrical classification task, a recall (R) of 0.86, a balanced accuracy (BA) of 0.92, and a precision (P) of 0.87 were obtained. For the quasi-symmetrical/quasi-asymmetrical classification task, R=0.77, BA=0.83, and P=0.70 were obtained. For the order of rotational symmetry detection task, the following performance was achieved: R=0.97, BA=0.98, and P=0.95 for a symmetrical set of curves, and R=0.98, BA=0.98, and P=0.90 for a quasi-symmetrical set of curves. We conclude our presentation demonstrating the usefulness of our methodology with three practical applications