Final answer:
Eukaryotic cells with mitochondria evolved after oxygen built up in the atmosphere due to endosymbiosis, where mitochondria were once free-living bacteria that were engulfed by larger prokaryotic cells.
Step-by-step explanation:
The theory of endosymbiosis suggests that eukaryotic cells with mitochondria evolved after oxygen built up in the atmosphere. According to this theory, mitochondria were once free-living bacteria that were engulfed by larger prokaryotic cells. Over time, a symbiotic relationship developed between the two organisms, with the larger cells providing a place for the smaller bacteria to live and in return receiving extra energy. As the atmosphere became oxygenated, the ancestral cells with mitochondria had an advantage and were able to metabolize oxygen for energy, leading to the evolution of eukaryotes with mitochondria.