We study thin aqueous films sandwiched between two oil phases (styrene). The system is stabilized by an anionic surfactant. These films exhibit stepwise thinning (stratification), due to the presence of micellar aggregates. By means of dynamic and static light scattering, we determine the hydrodynamic diameter and the aggregation number of the micelles. Using effective micellar volume fraction, we calculate the contribution of the oscillatory structural forces to the energy of interaction between the two film surfaces. Adding also the van der Waals and the electrostatic interactions, we are able to predict the contact angles of films which contain one layer of micelles. These angles are measured by interferometry, and the obtained experimental values agree very well with the theoretical estimates. It is proved that the oscillatory structural energy dominates in the total energy of interaction. The addition of electrolyte leads to smaller contact angles. This is unexpected in view of the conventional DLVO theory, which does not consider the oscillatory structural forces. Actually, at higher salt content the effective micellar diameter land volume fraction) decreases due to shrinkage of the electric double layer around each micelle. Therefore, the magnitude of the oscillatory structural energy diminishes, thus reducing the overall energy of attraction and the contact angle.