A trailer coupling with a ball support and a coupling ball arranged at a free end of the ball support. A coupling ball holder is fitted onto and can rotate on the coupling ball. A locking element is provided on the coupling ball holder by which the coupling ball holder is secured against being inadvertently removed from the coupling ball. An angle measuring device, provided on the coupling ball, comprises sensors which can detect rotation of the coupling ball holder relative to the coupling ball about a rotation axis. The position of the locking element, relative to the coupling ball, can be determined using the sensors.