Final answer:
Evidence for dark matter includes flat galactic rotation curves, gravitational lensing, and X-ray emissions from galaxy clusters, all indicating a mass greater than what is visible.
Step-by-step explanation:
We have substantial evidence for the existence of dark matter in individual galaxies and clusters, which include the anomalous rotation speeds of stars, gravitational lensing, and X-ray emissions from galaxy clusters. The rotation curves of galaxies, which remain flat instead of dropping off with distance from the galactic center, indicate the presence of more mass than is visible. These flat rotation curves imply a massive galactic halo of dark matter extending beyond the visible stars.
Additionally, the bending of light from distant objects due to gravitational lensing confirms dark matter's influence, as does the detection of X-ray emissions from hot ionized gas in galactic clusters, suggesting the presence of an unseen gravitational source.