The correct answer to this open question is the following.
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The excerpt from the Declaration of Independence that best demonstrates its connection to the Enlightenment ideal of natural rights is "Governments are instituted among Men."
The Declaration of Independence was promulgated on July 4, 1776, during the Revolutionary War of Independence.
The Declaration included innovative ideas from brilliant minds from the Enlightenment. We are talking about ideas on natural rights, liberty, and popular sovereignty. These ideas came from the minds of bright thinkers and philosophers like Voltaire, Jean-Jaques Rosseau, Thomas Hobbes, John Locke, and Baron of Montesquiou.