Question

If every pair of consecutive angles of a quadrilateral are supplementary, then the quadrilateral must be a parallelogram.

A. True

B. False

Answer 1

I believe this statement is true. 

Answer 2

Answer: true.

If a quadrilateral is a parallelogram, it has two sets of opposite sides that are congruent. If you follow the picture attacheed, you see that AD equals BC and AB equals DC.
There is a theorem that says that If a quadrilateral is a parallelogram, it has consecutive angles that are supplementary. Suplementary means that, those 2 angles together, form 180º.