Answer:
D) x = 22
Step-by-step explanation:
Given:
- ∠Z ≅ ∠X
- m∠W = 3x - 14
- m∠Y = x + 30
In a parallelogram, opposite angles are equal. Therefore, for figure WXYZ to be a parallelogram, the opposite angles W and Y must be congruent.
To find the value of x for which WXYZ must be parallelogram, set the expressions of the angles equal to each other and solve for x:
[tex]m\angle W = m\angle Y\\\\3x - 14 = x + 30\\\\3x - 14 - x = x + 30 - x\\\\2x - 14 = 30\\\\2x - 14 + 14 = 30 + 14\\\\2x = 44\\\\x = 22[/tex]
Therefore, the value of x for which WXYZ must be parallelogram is:
[tex]\LARGE\boxed{\boxed{x=22}}[/tex]
