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# Parallelogram Consecutive Angles Theorem

In a parallelogram, consecutive angles are supplementary.

The quadrilateral is a parallelogram. Then, by this theorem, the sum of the measures of its consecutive angles is

### Proof

Consider the parallelogram By definition, and and are parallel.

Since and are parallel and is a transversal, by the Consecutive Interior Angles Theorem, it can be stated that and are supplementary.

Therefore, this equation implies that the consecutive angles of a parallelogram are supplementary.