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So, in a parallelogram you have two sets of parallel lines. Take one set, and one of other lines and continue it beyond that set of two lines. Now, the single line is known as a tranversal, and by the same-side interior angles therom, the consecutive angles you are talking about must be congruent. The argument is the same on the opposite side. This is a lot easier with a diagram, ask your math teacher sometime.

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Q: What is the proof of The consecutive angles of a parallelogram are supplementary?
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