The tension of the three interfaces and the dihedral angle of the lens of the air/hexadecane lens/aqueous solution of tetramethylammonium dodecyl sulfate (TMADS) system were measured as a function of the surfactant concentration. The air/water surface tension vs concentration curves both with and without an oil lens exhibited a break point corresponding to the phase transition of the adsorbed films. From the thermodynamic analysis, it was shown that the phase transition drives the spreading of hexadecane molecules into the adsorbed film. The dihedral angle decreased very rapidly from about 50 degrees at zero concentration to about 6 degrees at the phase transition point and then increased slowly to about 20 degrees at the critical micelle concentration (cmc), suggesting the very drastic change in wetting properties at the phase transition point. The plausible gap was observed between the dihedral angles measured and those calculated from the interfacial tension values at the concentration range from just above the phase transition to near the cmc. This suggests a case where the Neumann relation does not hold even when a lens exists stably. One of the possibilities may be that the wetting film is rather thick just above the phase transition point.