© 2016 ESO. We report on the analysis of the broad Fe Kα line feature of Cyg X-1 in the spectra of four simultaneous hard intermediate state observations made with the X-ray Multiple Mirror mission (XMM-Newton), the Rossi X-ray Timing Explorer (RXTE), and the International Gamma-Ray Astrophysics Laboratory (INTEGRAL). The high quality of the XMM-Newton data taken in the Modified Timing Mode of the EPIC-pn camera provides a great opportunity to investigate the broadened Fe Kα reflection line at 6.4 keV with a very high signal to noise ratio. The 4-500 keV energy range is used to constrain the underlying continuum and the reflection at higher energies. We first investigate the data by applying a phenomenological model that consists of the sum of an exponentially cutoff power law and relativistically smeared reflection. Additionally, we apply a more physical approach and model the irradiation of the accretion disk directly from the lamp post geometry. All four observations show consistent values for the black hole parameters with a spin of a ~ 0.9, in agreement with recent measurements from reflection and disk continuum fitting. The inclination is found to be i ~30°, consistent with the orbital inclination and different from inclination measurements made during the soft state, which show a higher inclination. We speculate that the difference between the inclination measurements is due to changes in the inner region of the accretion disk.