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Rule

Parallelogram Consecutive Angles Theorem

In a parallelogram, consecutive angles are supplementary.

The quadrilateral $P Q R S$ is a parallelogram. Then, by this theorem, the sum of the measures of its consecutive angles is $18 0^{\circ} .$

$x^{\circ} + y^{\circ} = 18 0^{\circ}$

Proof

Consider the parallelogram $P Q R S .$ By definition, and $\overline{Q R}$ and $\overline{P S}$ are parallel.

Since $\overline{P S}$ and $\overline{Q R}$ are parallel and $\overline{P Q}$ is a transversal, by the Consecutive Interior Angles Theorem, it can be stated that $∠ P$ and $∠ Q$ are supplementary.

$x^{\circ} + y^{\circ} = 18 0^{\circ}$

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

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Proof