We analyze the energy autocorrelation functions and the energy coherence lengths in the strongly dissipative collision 28 Si(E lab = 130 MeV) + 48 Ti for Z = 11 and 12 reaction fragments. It is found that in order to obtain a good fit of both the energy-averaged angular distributions and the angular dependence of the energy coherence lengths one has to take into account (i) the dissipation and fluctuation of the relative angular momentum of the dinucleus and (ii) the contribution from direct (fast) reactions in addition to the statistical (relative slow) interaction processes. The established angular dependence is a direct consequence of the angular-momentum dissipation-fluctuation effects on the time-space evolution of the intermediate dinucleus.