Geometry

Question Analysis:
This question involves checking whether a quadrilateral is a parallelogram by applying the property that the diagonals bisect each other.
The main focus is verifying if both diagonals are bisected at the same value of x.

Key Concept Explanation:
In a parallelogram, the diagonals bisect each other. This means:
WO = OY
XO = OZ
Only when both equalities hold true for the same value of x, can we say that WXYZ is a parallelogram.

Step-by-Step Solution:
Step 1: Set WO = OY
3x − 4 = x + 8 ⇒ 2x = 12 ⇒ x = 6
Step 2: Set XO = OZ
2x + 5 = 4x − 7 ⇒ −2x = −12 ⇒ x = 6

Common Mistakes:
Solving only one equation instead of both
Mixing up diagonal segments
Ignoring that both equalities must hold for the same x

Summary:
To determine whether a quadrilateral ...