The anisotropy in the angular distribution of the fusion-fission and quasifission fragments for the 16O + 238U , 19F + 208Pb and 32S + 208Pb reactions is studied by analyzing the angular-momentum distributions of the dinuclear system and compound nucleus which are formed after capture and complete fusion, respectively. The orientation angles of the axial symmetry axes of the colliding nuclei relative to the beam direction are taken into account for the calculation of the variance of the projection of the total spin onto the fission axis. It is shown that there is a large contribution of the quasifission fragments in the 32S + 208Pb reaction to the deviation of the experimental angular anisotropy from the statistical model results. Enhancement of anisotropy at low energies in the 16O + 238U reaction is connected with the quasifission of the dinuclear system having low temperature and relatively small effective moment of inertia.