Geometry

Question Analysis：
This problem requires applying the adjacent angle property to determine when a quadrilateral could be a parallelogram.

Key Concept Explanation：
For adjacent angles in parallelograms：
• Must sum to 180° (supplementary)
• This creates parallel sides through consecutive interior angles theorem

Step-by-Step Solution：
Set up equation：
(5x - 10) + (2x + 50) = 180
Simplify and solve：
7x + 40 = 180 → 7x = 140 → x = 20
Verification：
∠A = 5(20)-10 = 90°
∠D = 2(20)+50 = 90°
90° + 90° = 180° (valid...