Quadrilateral ABCD has side lengths of AB = 2z + 2, BC = 8, CD = 5z – 10, and AD = 8. Find the value of z for which quadrilateral ABCD is a parallelogram.

In a parallelogram, opposite sides have equal lengths. Since BC and AD are both 8, that pair already matches; set the other opposite sides equal: 2z + 2 = 5z − 10. Solving gives 12 = 3z, so z = 4. The correct choice is D, 4.

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