Geometry

Question Analysis：
This problem requires using the adjacent angle property of parallelograms to solve for the variable x.

Key Concept Explanation：
For a quadrilateral to be a parallelogram：
• Adjacent angles must be supplementary (sum to 180°)
• This creates parallel sides through the consecutive interior angles theorem

Step-by-Step Solution：
∠D = ∠B → ∠A + ∠D = ∠A + ∠B
Set up the adjacent angles equation：
(4x - 15) + (x + 45) = 180
Simplify and solve：
5x + 30 = 180 → 5x = 150 → x = 30
Verification：
∠A = 4(30) - 15 = 105°
∠D = ∠B = 30 + 45 = 75°
105° + 75° = 180° (satisfies parallelogram condition)

Common Mistakes：
• Forgetting to set th...