In studies of the giant magnetoresistance (GMR) of ferromagnetic/ nonmagnetic/ferromagnetic sandwich films, both the anisotropic magnetoresistance (AMR) and the GMR change with the angle between the magnetizations of the individual layers when the current direction is fixed. A technique is presented that separates the two phenomena and shows explicitly the angular dependence of the GMR. The technique relies on layered films in which the magnetization of one or more layers is held fixed by an exchange biasing field and the magnetization of another layer is rotated by an applied field. The separation of the two magnetoresistance contributions takes advantage of the fact that the GMR has a cosine angular dependence and the AMR of the rotated layer has a cosine squared angular dependence. The results indicate the GMR can be isolated from the AMR using only data containing contributions from both.