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We report on unexpected field-angle dependence of magnetoresistance measurements of commercial, high-purity Nb discovered during our study of residual resistivity ratio (RRR) measurements. The RRR value indicates the purity and the low-temperature thermal conductivity of the Nb and is used as a specification for superconducting radio-frequency cavities. The RRR is typically defined as the ratio of the electrical resistivities measured at 273 K and 4.2 K. One way to obtain the normal-state resistivity at 4.2 K is to measure the resistivity versus magnetic field at 4.2 K and extrapolate to zero field. The field-angle dependence was measured when a specimen was rotated while the field was transverse to the specimen current. The resistance changed by about 10% as the angle varied at 8 T and the local maxima and minima of the resistance were separated by about 30°. This was observed on three polycrystalline Nb bar specimens with nominal dimensions of 64 mm × 6.7 mm × 3.3 mm and voltage taps separated by 30 mm. A similar field-angle dependence was obtained on a polycrystalline Cu wire specimen. This phenomenon has implications for Nb RRR measurements and interlaboratory comparisons.