The correlation between Si-29 chemical shifts and Si-O-Si bond angles in SiO2 is determined within density-functional theory for the full range of angles present in vitreous silica. This relation closely reproduces measured shifts of crystalline polymorphs. The knowledge of the correlation allows us to reliably extract from the experimental NMR spectrum the mean (151 degrees) and the standard deviation (11 degrees) of the Si-O-Si angular distribution of vitreous silica. In particular, we show that the Mozzi-Warren Si-O-Si angular distribution is not consistent with the NMR data. This analysis illustrates the potential of our approach for structural determinations of silicate glasses.