The morphology of liquid liquid phase separated aerosols has a strong impact on their rate of gas and water uptake, and the type and rate of heterogeneous reactions in the atmosphere. However, it is extremely challenging to experimentally distinguish different morphologies (core shell or partial wetting) of aerosols and to quantify the extent of wetting between the two phases. The aim of this work is to quantitatively predict the morphology of liquid liquid aerosols from fundamental physical properties of the aerosol phases. We determine the equilibrium structure of liquid liquid phase separated aerosols through free energy minimization and predict that the contact angle between the two liquids in the aerosol depends on the composition but not the amount of each phase. We demonstrate that for aerosols of diameter larger than similar to 100 nm, the equilibrium contact angle can be accurately predicted from the surface tensions of each liquid with the vapor and between the two liquids through an expression that is identical to Young's equation. The internal.structure of smaller, ultrafine aerosols depends also on the value of the line tension between the two liquids and the vapor. The thermodynamic model accurately predicts the experimental morphology, core shell or partial wetting, of all aerosols for which surface tensions are provided in the literature, and provides contact angles that cannot be accurately determined with state of the art experimental methods. We find that the contact angle of model atmospheric aerosols is rarely higher than 30 degrees. We validate the thermodynamic predictions through molecular simulations of nonane-water droplets, and use the simulation data to compute line tension values that are in good agreement with theory and the analysis from experimental data in water nonane droplets. Our finding of a simple analytical equation to compute the contact angle of liquid liquid droplets should have broad application for the prediction of the morphology of two-phase atmospheric aerosols and its impact in their chemistry.