We studied by angle-resolved photoelectron spectroscopy the strain-related structural transition from a pseudomorphic monolayer (ML) to a striped incommensurate phase in an Ag thin film grown on Pt(111). We exploited the surfactant properties of Bi to grow ordered Pt(111)-xMLAg-Bi trilayers with 0 <= x <= 5 ML, and monitored the dispersion of the Bi-derived interface states to probe the structure of the underlying Ag film. We find that their symmetry changes from threefold to sixfold and back to threefold in the Ag coverage range studied. Together with previous scanning tunneling microscopy and photoelectron diffraction data, these results provide a consistent microscopic description of the coverage-dependent structural transition.