Final answer:
The value of x that makes WXYZ a parallelogram is 6, found by setting the opposite angles equal to each other (5x - 4 = 2x + 14) and solving for x.
Step-by-step explanation:
To find the value of x for which quadrilateral WXYZ is a parallelogram, we must use the properties of a parallelogram that dictate opposite sides are parallel and equal in measure. Since Z=X by definition, then the angles at vertices W and Y are equal because they are opposite angles in the parallelogram. The equation given as mW = 5x - 4 and mY = 2x + 14 represent the measures of angles W and Y, respectively. Setting these equal to each other because opposite angles in a parallelogram are congruent, we get:
Solving for x:
- 5x - 2x = 14 + 4
- 3x = 18
- x = 6
Therefore, the value of x for which WXYZ is a parallelogram is 6.