We investigate the symmetry-breaking effects of magnetic nanostructures that present unidirectional (one-fold) magnetic anisotropy. Angular and field dependent transport and magnetic properties have been studied in two different exchange-biased systems, i.e. ferromagnetic (FM)/ antiferromagnetic (AFM) bilayer and spin-valve structures. We experimentally show the direct relationships between the magnetoresistance (MR) response and the magnetization reversal pathways for any field value and direction. We demonstrate that even though the MR signals are related to different transport phenomena, namely anisotropic magnetoresistance (AMR) and giant magnetoresistance (GMR), chiral asymmetries are found around the magnetization hard-axis direction, in both cases originated from the one-fold symmetry of the interfacial exchange coupling. Our results indicate that the chiral asymmetry of transport and magnetic behaviors are intrinsic of systems with an unidirectional contribution