Geometry

Question Analysis:
This question uses the geometric property of parallelograms that opposite sides are congruent.
The main focus is applying this concept algebraically to find the value of x.

Key Concept Explanation:
In any parallelogram, both pairs of opposite sides are equal in length:
PQ ≅ RS
QR ≅ PS
We form two equations using these congruent sides and solve for x.

Step-by-Step Solution:
Set PQ = RS:
→ 5x – 7 = 3x + 1
→ 2x = 8
→ x = 4 
Set QR = PS:
→ 4x + 2 = 2x + 10
→ 2x = 8
→ x = 4 
 Both conditions satisfied at x = 4

Common Mistakes:
Only checking one pair of opposit...