Gearboxes are used in a wide range of industrial applications to facilitate the transmission of rotational movement. The occurrence of unanticipated gearbox failures can result in the complete standstill of entire systems, thereby reducing their availability. Consequently, there has been a growing tendency in industrial applications to monitor gearboxes with externally applied acceleration sensors. The acceleration sensors acquire vibrations on the gearbox housing in order to detect damages. This technology has been demonstrated to be effective in the detection of gearbox damage. However, the long transfer path from the gear damage via the shaft and bearings to the housing results in a reduction in the amount of usable damage information and can be superimposed by external disturbances. In recent years, rotational angle measurement has emerged as a promising alternative to vibration measurement in the academic field. Rotational angle measurement can be used to measure the instantaneous angular speed and the transmission error. In comparison to externally applied acceleration sensors, these techniques offer the potential to make more precise predictions about damages, with the possibility of determining it at an earlier stage and with greater accuracy. Furthermore, the additional rotational angle information enables damages to be detected at transient speeds. Furthermore, the measurement of transmission error enables the quantification of damages, a process that was previously only possible through manual inspection of the gears. Despite the outlined advantages, these techniques have thus far only been used to a limited extent in industrial applications. Reasons for this are the high cost of the optical rotational angle sensors that are most commonly used and the necessity of making design changes when mounting the angle sensor. In this thesis, a measuring device is therefore developed that can be integrated to measure the rotational angle of gearboxes without the necessity of modifying the design of the rotating gear elements. The proposed measuring system uses the helical gear wheel of a gearbox as a material measure to measure the rotational angle with a magnetoresistive sensor. The impact of utilising the gear wheel on the accuracy of the measurement is analysed, and the dependencies on operational conditions are investigated. The suitability of the measuring device for damage detection is then analysed on two test rigs. The results of the damage detection are compared with those obtained using acceleration sensors and reference rotational angle sensors. Firstly, the basic suitability of the measuring device for damage detection is analysed using artificial damages. Subsequently, a number of artificial damage tests are used for the purpose of damage classification using a machine learning approach. The aforementioned results are then subjected to a long-term fatigue test, during which real pitting damage is generated. The fatigue test is employed to illustrate the viability of the measuring device for the detection of real damages. Finally, the potential of the measuring device for measuring the absolute rotational angle and the torque of a gear stage is demonstrated, thereby providing the basis for predictive maintenance approaches.