Geometry

Question Analysis：
This question tests understanding of which condition definitively proves a quadrilateral is a parallelogram.

Key Concept Explanation：
The sufficient condition to prove a parallelogram using angles is：
• Both pairs of adjacent angles being supplementary
This automatically makes opposite sides parallel

Step-by-Step Solution：
The critical condition is adjacent angles summing to 180°：
(2y + 10) + (3y - 20) = 180
Solve： 5y - 10 = 180 → y = 38
At y=38：
∠E = 86° and ∠F = 94° → sum to 180°
Ang ∠F = ∠H
This would force the other adjacent pairs to also be supplementary

Common Mistak...