We have measured the in-plane angular variation of nucleation and annihilation fields of a multidomain magnetic single dot with a micro-SQUID. The dots are Fe/Mo(110) self-assembled in ultrahigh vacuum, with submicron size and an elongated hexagonal shape. The angular variations were quantitatively reproduced by micromagnetic simulations. Discontinuities in the variations are observed, and shown to result from bifurcations related to the interplay of the nonuniform magnetization state with the shape of the dot.