An angle measuring system includes a first component group and a second component group, the first component group being mounted in a manner allowing rotation about an axis relative to the second component group. The first component group includes a ring having a running surface and an angle scaling. The second component group has a further ring having a further running surface, as well as a sensor for scanning the angle scaling. Rolling elements are arranged between the running surfaces, the angle scaling being applied such that a geometric pattern of the angle scaling in a first region differs from a geometric pattern of the angle scaling in a second region as a function of radial runouts of the running surfaces and/or of the rolling elements.