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Rule

Parallelogram Consecutive Angles Theorem

In a parallelogram, consecutive angles are supplementary.
A parallelogram PQRS

The quadrilateral PQRS is a parallelogram. Then, by this theorem, the sum of the measures of its consecutive angles is 180^(∘).


x^(∘)+ y^(∘) = 180 ^(∘)

Proof

Consider the parallelogram PQRS. By definition, and QR and PS are parallel.

A parallelogram PQRS

Since PS and QR are parallel and PQ is a transversal, by the Consecutive Interior Angles Theorem, it can be stated that ∠ P and ∠ Q are supplementary.


x^(∘) + y^(∘) = 180^(∘)

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

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