Question

If consecutive angles of a quadrilateral are supplementary, is the quadrilateral always a parallelogram? Explain your reasoning.

Answer 1

Yes, if all pairs of consecutive angles are supplementary, the quadrilateral is a parallelogram.

No, if only one pair of consecutive angles is supplementary, the quadrilateral may be trapezoid, and is not necessarily a parallelogram.

Step-by-step explanation:

All pairs of consecutive angles being supplementary ensures opposite sides are parallel. (Consecutive angles are same-side interior angles.) If opposite sides of a quadrilateral are parallel, that quadrilateral is a parallelogram.

If one pair of consecutive angles is supplementary, then at least two sides of the quadrilateral are parallel. The figure may be a trapezoid, not a parallelogram.

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Comment on the question

We consider the problem statement to be ambiguous regarding the number of consecutive angles. Use the answer appropriate to your interpretation of the question.

Answer 2

No

Step-by-step explanation:

The problem never said that all of the pairs of consecutive angles of the quadrilateral were supplementary. If only 1 pair of consecutive angles were supplementary, it could be a right trapezoid, which is definitely not a parallelogram.