Geometry

Question Analysis:
This problem applies two key properties of parallelograms: adjacent angles are supplementary, and opposite angles are equal.
Students must set up and solve an equation to find the missing angle.

Key Concept Explanation:
In any parallelogram:
Adjacent angles are supplementary (add to 180°)
Opposite angles are equal in measure
All interior angles sum to 360°

Step-by-Step Solution:
Identify angles P and Q as adjacent angles (they share side PQ)
Set up equation: (3x + 10) + (2x + 30) = 180
Combine like terms: 5x + 40 = 180
Solve for x: 5x = 140 → x = 28
Find angle P: 3(28) + 10 = 94°
Find angle Q: 2(28) + 30 = 86° (verification: 94° + 86° = 180°)
Angle R is opposite angle P → angle R = ang...