Orientations of single-element extensions of graphic matroids

Slilaty and Zaslavsky (2024) characterized all single-element extensions of graphic matroids in terms of a graphical structure called a cobiased graph. In this paper we characterize all orientations of a single-element extension of a graphic matroid in terms of graphically defined orientations of its associated cobiased graph. We also explain how these orientations can be canonically understood as dual to orientations of biased graphs if and only if the underlying graph is planar.