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In the present work, the results of theoretical investigations of the interaction acoustic waves with a layered structure containing layer of polydisperse bubbly liquid at different angles of incidence are presented. The layered structure is a thin layer containing a gel with air bubbles enclosed between two layers of polycarbonate small thickness. The theoretical model for calculating the evolution of the acoustic signal transmitted through such a layered structure is presented. This model includes a continuum model of the dynamics of bubble liquid, a simple model for calculating the transmission coefficient of the plane monochromatic wave through the layered structure taking into account the angle of incidence and a method of the discrete Fourier for the numerical calculation of the dynamics of pulse pressure perturbation. It is allows to evaluate the transmission and reflection coefficients depending on the availability of bubbles in the liquid layer and the angle of incidence of the acoustic wave. It is shown that the availability of polydisperse air bubbles in the gel layer substantially changes the transmission and reflection of the acoustic waves at frequencies lower than or close to the Minnaert resonance frequency of bubbles with a characteristic average radius of the bubble size distribution. This is due to fact that for an acoustic wave with frequency close to the Minnaert resonance frequency of bubbles exist resonance dispersion of sound caused by resonant dependence compressibility of bubble medium from pressure vibrations frequency. Also, the availability of bubbles manifests itself in the band of the acoustic opacity of bubble liquid. This is frequency range above the resonance frequency where the phase velocity and attenuation coefficient take the abnormally high values. It was found that for frequencies less than twice the Minnaert resonance frequency dependence of the transmission coefficient from the angle of incidence is not significant. In this frequency range the transmission and reflection of acoustic waves is influenced by the size of the bubbles, their volume content and their thermophysical properties. The dynamics of the acoustic signal after transmission through the three-layered structure at different angles of incidence is calculated. Results of these calculations in the special case of normal incidence of the acoustic signal are in good agreement with known experimental data.