The angular distribution of the inelastic scattering of photons at low energies (≤80 KeV) has been measured in organic material, soil, rocks, wood, steel sheet, and water. The measurements have been performed under air inside an X-ray shield cabinet using X-rays tube as a photon source and a thermoelectrically cooled CdTe detector. Measurements have been taken for both single and combined materials. The contributions of inelastic scattering of photons for the lower Z material in a given configuration have been extracted. The measured signal is primarily Compton scattering. The measured inelastic scattering contributions were compared with the calculated inelastic scattering cross sections according to the Klein-Nishina theory, updated to include a practical energy distribution of an X-ray tube beam. Relatively good agreement was found for all targets under investigation. The slight discrepancy is attributed to photoelectric effect and sample configuration. Present results may act as a guide for optimization of X-ray imaging sensors and in particular of those based on lobster eye X-ray optics suitable for cargo inspection, improvised explosives detection, non-destructive evaluation, and medical imaging.