A theoretical study of photoelectron angle distribution in processes of photoionization sodium metal cluster anions is done. A consistent many-body theory based on the jellium model is applied to the description of angular resolved photoelectron spectra of metal clusters anions and the results of calculations demonstrate the dominant role of the many-body effects in the formation of angular distributions of photoelectrons emitted from sodium clusters and are in a good agreement with recent experimental data. The concrete comparison of theory and experiment has been performed for the photoionization of «magic» sodium clusters Na7~, Na|9~, Na57~-anions being characterized by the entirely closed shells of delocalized electrons.