This paper presents a general method for modeling extended-reaction surface impedance boundary conditions in time-domain wave-based room acoustic simulations. A sound field separation technique is used to separate the sound field at a boundary into its incident and reflected components, in each time step of the simulation. Once separated, the incidence angle of the incident sound field is determined and the boundary surface impedance is adjusted accordingly. This allows for the incorporation of angle dependent properties of extended-reaction room surfaces in the simulation. The proposed method is validated both analytically and experimentally. An excellent agreement is found between simulations and analytic and measured reference data. Furthermore, a significant improvement in accuracy is observed, when comparing the extended-reaction model to the commonly used local-reaction model, particularly for surface types which exhibit strong extended-reaction behavior. A room with a suspended porous ceiling is simulated using local- and extended-reaction models, where large and perceptually noticeable differences are found, indicating the importance of including extended-reaction behavior in simulations of room acoustics.