Final answer:
The Enlightenment ideas threatened the old systems of government and church by challenging divine right monarchies, promoting individual rights and the separation of church and state, and sparking a shift towards popular sovereignty.
Step-by-step explanation:
The Enlightenment ideas threatened the old systems of government and church for several reasons. Firstly, the Enlightenment brought new beliefs on how government should be established and conducted, challenging the divine right monarchies that were common in Europe during the 17th and 18th centuries. Philosophers like John Locke asserted that people had the right to change a government that did not protect their natural rights, which contradicted the centuries-old traditions of political-social order.
Secondly, the Enlightenment promoted concepts such as individual rights, equality, and the separation of church and state. These ideas challenged the privileges enjoyed by the nobility and the traditional dominance of the Catholic Church. Enlightenment thinkers sought to curtail the political power of organized religion and dismantle the restrictive social structures associated with it.
Lastly, the Enlightenment sparked a shift in people's understanding of political sovereignty. It encouraged the idea of popular sovereignty and government by consent of the governed, challenging the belief in the divine right of kings. These ideas of individual rights, equality, and popular sovereignty eventually influenced major revolutions like the French Revolution and the American Revolution.