The correct statement that analyzes how Enlightenment thinker Thomas Hobbes’s ideas impacted the American Revolution is:
Colonists felt that their agreement with the king had been broken when he violated their rights.
This reflects Hobbes's social contract theory, where the legitimacy of a ruler's authority depends on their protection of the people's rights. When these rights were perceived to be threatened, colonists believed their agreement with the king was violated, leading to revolution.