Geometry

Question Analysis
This question tests whether supplementary adjacent angles are sufficient to prove a quadrilateral is a parallelogram.

Key Concept Explanation
If both pairs of adjacent angles are supplementary, opposite sides must be parallel, making it a parallelogram.
This is a stronger condition than just one pair being supplementary.

Step-by-Step Solution
Given:
∠W + ∠X = 180° → WX // YZ
∠X + ∠Y = 180° → XY // WZ
Conclusion: Both pairs of opposite sides are parallel, so WXYZ is a parallelogram.

Option Analysis
A: Incorrect (opposite angles will automatically be equal if adjacent angles are supplementary)
B: Correct (both pairs of adjacent angles being supplementary guarantees a parallelogram)
C: Unnecessary condition