Geometry

Question Analysis：
This problem combines algebraic expressions with parallelogram angle conditions to determine a missing variable.

Key Concept Explanation：
For a quadrilateral to be a parallelogram：
• Adjacent angles must be supplementary (sum to 180°)
• Opposite angles must be equal

Step-by-Step Solution：
First solve for x using adjacent angles ∠A + ∠B = 180°：
(3x + 20) + (2x + 40) = 180 → 5x + 60 = 180 → x = 24
Find ∠A = 3(24) + 20 = 92° and ∠B = 2(24) + 40 = 88°
For parallelogram, opposite angles must be equal.
So ∠C = ∠A = 92°：
5y - 10 = 92 → 5y = 102 → y = 20.4

Common M...