In quadrilateral ABCD, AD ∥ BC. Quadrilateral A B C D is shown. Sides A D and B C are parallel. The length of A D is 3 x + 7 and the length of B C is 5 x minus 9. What must the length of segment AD be for the quadrilateral to be a parallelogram? 8 units 16 units 31 units 62 unitsIn quadrilateral ABCD, AD ∥ BC. 9.

  31 units

Step-by-step explanation:

When the figure is a parallelogram, opposite sides have the same measure:

  AD = BC

  3x +7 = 5x -9 . . . . . . substitute given expressions

  16 = 2x . . . . . . . . . . . add 9-3x

  8 = x . . . . . . . . . . . . . divide by 2

Use this value of x in the expression for AD to find its required length:

  AD = 3(8) +7 = 24 +7

  AD = 31 . . . . units

The length of segment AD must be 31 units for ABCD to be a parallelogram.