We probe the production of single and double K-shell vacancies in xenon atoms during symmetric collisions with Xe54+ ions at 95, 146, and 197 MeV/u at the heavy-ion storage ring equipped with an internal gas-jet target. For each collision energy, the xenon Kα x-ray spectra are measured at five observation angles, ranging from 35° to 145° with respect to the projectile beam. To resolve the measured Xe target Kα x-ray spectra into four Gaussian peaks, including the hypersatellites and satellites of the Kα2,1 lines, we develop a data-analysis method that reduces the fitting parameters from 12 to 6. The determined intensities of the hypersatellites and satellites, which shows no significant radiation anisotropy, are subsequently used to calculate the cross-section ratio R21 for double-to-single K-shell vacancy production in the Xe target atoms. The obtained R21 values decrease from 0.286 ± 0.036 to 0.176 ± 0.021 as the collision energy increases. We compare these experimental results to relativistic time-dependent two-center calculations and find reasonable agreement between the theoretical predictions and the experimental data