We have studied the compositional dependence of the microstructure of rubidium berate glasses, (Rb2O)(x)(B2O3)(1-x), by means of dynamic angle spinning (DAS) NMR spectroscopy of boron-ll. Our NMR spectra simultaneously resolve three distinct boron sites, which we assign to boroxol rings, BO3 groups that are not in rings, and tetrahedral BO4 groups. These assignments are based on isotropic and anisotropic shifts of the sites in different magnetic fields and on comparison to the boron-ll DAS NMR spectra of polycrystalline berates of,known structure. We observe an essentially constant fraction of boron atoms in the boroxol rings as a function of modifier concentration. In contrast, the fraction of boron atoms in nonring BO3 sites is reduced as the Rb2O concentration increases, while the population of the fourfold coordinate site increases. The compositional dependence we observe, and its dependence on the thermal history of the glass, suggests that the boroxol ring is an especially stable structure.