Results on the magneto-optical investigation of magnetic and magneto-optical properties Fe/Pt/Fe trilayers and sandwiches with wedge-shaped Fe and Pt layers are presented. The oscillatory behavior of the saturation field of trilayers with changing the Pt-layer thickness was discovered. That was explained by the presence of the exchange coupling between Fe-layers through Pt-spacer. It was established that in the sandwiches, transverse Kerr effect (TKE) oscillates along Pt-thickness periodically. The period of the oscillations is equal to similar to1 - 1.5 mn. The strong Pt layer influence on TKE spectra of the samples was revealed. The discovered peculiarities of magnetic and magnetooptical properties of Fe/Pt thin-film structures were ascribed to the spin-polarized Quantum Well States in the Pt-layer.