Which best explains if quadrilateral WXYZ can be a parallelogram?

a) WXYZ can be a parallelogram with one pair of sides measuring 15 mm and the other pair measuring 9 mm.

b) WXYZ can be a parallelogram with one pair of sides measuring 15 mm and the other pair measuring 7 mm.

c) WXYZ cannot be a parallelogram because there are three different values for x when each expression is set equal to 15.

d) 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.

Solution:

Assuming WXYZ is a parallelogram

then the side (x + 8) must equal 15 (since,opposite sides of a parallelogram are equal)

x + 8 = 15

x = 15 - 8 = 7

Now, we will substitute 7 into the other pair of opposite sides

Substituting in x + 2 we get 7 + 2 = 9

Substituting in 2x - 5 we get (7 × 2) - 5 = 14 - 5 = 9

Hence, the other pair of opposite sides are also equal i.e., 9mm

Thus, Option (a) is the right answer.

Which best explains if quadrilateral WXYZ can be a parallelogram?

Summary:

Option (a) - WXYZ can be a parallelogram with one pair of sides measuring 15 mm and the other pair measuring 9 mm