We investigate magnetization damping in symmetric NiFe/Ru/NiFe synthetic antiferromagnet using broadband ferromagnetic resonance. The field and frequency linewidth for both, acoustic and optical modes, were measured all along the dispersion relation. These results were compared with a model based on the Landau Lifshitz Gilbert equation. We show that this model explains most of the features observed in the field linewidth measurements, however the phenomenological inhomogeneous linewidth is necessary to fully explain the results. The measured damping parameter for the acoustic mode is in agreement with the intrinsic damping for NiFe, while for the optical mode and enhanced Gilbert damping due to the spin pumping effects was obtained.