We instigate the angle-dependent magnetoresistance (AMR) of the layered nodal-line Dirac semimetal ZrSiS for the in-plane and out-of-plane current directions. This material has recently revealed an intriguing butterfly-shaped in-plane AMR whose origin is not well understood. Our aim was to understand the mechanism behind this peculiar shape of AMR and also to probe AMR in the out-of-plane current direction. In contrast to the in-plane AMR, the polar out-of-plane AMR shows a surprisingly different response with a pronounced cusplike feature. The maximum of the cusplike anisotropy is reached when the magnetic field is oriented in the a-b plane. Moreover, the AMR for the azimuthal out-of-plane current direction exhibits a very strong fourfold a-b plane anisotropy. Combining the Fermi surfaces calculated from first principles with the Boltzmann's semiclassical transport theory, we reproduce all the prominent features of the unusual behavior of the in-plane and out-of-plane AMR. We can conclude that the dominant contribution the cusplike AMR lies in open orbits of the hole pocket and, in general, AMR is strongly influenced by charge compensation effect and the off-diagonal conductivity tensor elements, which give rise to peculiar butterfly-shaped AMR. Finally, the semiclassical model was also able to clarify the origin of strong nonsaturating (subquadratic) transverse magnetoresistance observed in this material, as an effect of imperfect charge-carrier compensation and open orbits.