We present a systematic study of the anisotropy configuration effects on the magnetic properties of exchange-biased ferromagnetic/antiferromagnetic (FM/AFM) Co/IrMn bilayers. The interfacial unidirectional anisotropy is set extrinsically via a field cooling procedure with the magnetic field misaligned by an angle βFC with respect to the intrinsic FM uniaxial anisotropy. High resolution angular dependence in-plane resolved Kerr magnetometry measurements have been performed for three different anisotropy arrangements, including collinear βFC=0∘ and two opposite noncollinear cases. The symmetry breaking of the induced noncollinear configurations results in a peculiar nonsymmetric magnetic behavior of the angular dependence of magnetization reversal, coercivity, and exchange bias. The experimental results are well reproduced without any fitting parameter by using a simple model including the induced anisotropy configuration. Our finding highlights the importance of the relative angle between anisotropies in order to properly account for the magnetic properties of exchange-biased FM/AFM systems.