We theoretically investigate the energy and the angular-resolved cross section for the photoelectron emission from a hexagonal monolayer of a C₆₀ fullerene physisorbed on an inert substrate. On the basis of a tight-binding scheme with an on-site shell model for the single molecules we evaluate the energy and angular spectra of the photoelectrons upon the absorption of VUV linearly polarized photons. A symmetry analysis provides a clear interpretation of the observed structures in the numerically calculated cross sections. When the photoelectron is temporarily captured within the molecular cage, the symmetry of the angular emission pattern is mainly determined by the symmetry of the single fullerene molecule. In contrast, for the photoelectron state mainly located outside the C₆₀ the angular dependence of the photoemission reproduces the symmetry of the lattice. These changes of the angular patterns repeat concurrently with the oscillations of the angle-integrated cross section.