How did Louis XIV use religious ideas to legitimize his
rule?

Louis XIV was able to use the religious idea of the Divine Right of Kings to legitimize his rule.

Louis XIV subscribed to the Divine Right of Kings which stated that:

In asserting this right, he ruled without having a Chief Minister. It seemed to work for him however, because he was a relatively good king who modernized French taxation laws, improved trade and encouraged art.

In conclusion, Louis believed that he had the right to do whatever he wanted because he was God's chosen representative to rule France.

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your answer would be (b)

your mothers brothers brother in law would be your father.