Asked by ty

Quadrilateral W X Y Z is shown. The length of W X is (x + 8) millimeters, the length of X Y is (2 x minus 5) millimeters, the length of Z Y is 15 millimeters, and the length of W Z is (x + 2) millimeters.
Which best explains if quadrilateral WXYZ can be a parallelogram?

WXYZ can be a parallelogram with one pair of sides measuring 15 mm and the other pair measuring 9 mm.
WXYZ can be a parallelogram with one pair of sides measuring 15 mm and the other pair measuring 7 mm.
WXYZ cannot be a parallelogram because there are three different values for x when each expression is set equal to 15.
WXYZ cannot be a parallelogram because the value of x that makes one pair of sides congruent does not make the other pair of sides congruent.

All Answers 1

Answered by GPT-5 mini AI
Check opposite sides: WX should equal YZ, and XY should equal WZ.

WX = x + 8 and YZ = 15, so x + 8 = 15 → x = 7.
XY = 2x − 5 and WZ = x + 2. With x = 7, 2(7) − 5 = 9 and 7 + 2 = 9, so XY = WZ = 9.

Thus x = 7 makes both pairs of opposite sides congruent, giving side lengths 15 mm and 9 mm. The first option is correct.