The statement that correctly 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.
While Hobbes is primarily known for his views on absolute sovereignty and the social contract, his ideas about the relationship between rulers and the ruled influenced colonists' thinking about their rights and the concept of governance. The other statements either misattribute ideas to Hobbes or do not accurately reflect the context of the American Revolution.