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A detailed study of the angular dependence of the magnetization reversal in polycrystalline ferromagnetic (FM)/antiferromagnetic Co/IrMn bilayers with noncollinear FM and unidirectional anisotropies shows a peculiar asymmetric magnetic behavior. The anisotropy configuration is set via a field cooling (FC) procedure with the magnetic field misaligned with respect to the easy magnetization direction of the FM layer. Different magnetization reversal modes are observed for either positive or negative angles with respect to the FC direction. The angular dependence of both coercivity and exchange bias also clearly displays the broken symmetry of the induced noncollinearity. Our findings are reproduced with a modified Stoner-Wohlfarth model including the induced anisotropy configuration. Our results highlight the importance of the relative angle between anisotropies in exchange bias systems, opening a new path for the tailoring of their magnetic properties.