Transport coefficients of correlated electron systems are often useful for mapping hidden phases with distinct symmetries. Here we report a transport signature of spontaneous symmetry breaking in the magnetic Weyl semimetal cerium-aluminum-germanium (CeAlGe) system in the form of singular angular magnetoresistance (SAMR). This angular response exceeding 1000% per radian is confined along the high-symmetry axes with a full width at half maximum reaching less than 1° and is tunable via isoelectronic partial substitution of silicon for germanium. The SAMR phenomena is explained theoretically as a consequence of controllable high-resistance domain walls, arising from the breaking of magnetic point group symmetry strongly coupled to a nearly nodal electronic structure. This study indicates ingredients for engineering magnetic materials with high angular sensitivity by lattice and site symmetries.