Answer:
The value of x that makes the quadrilateral a parallelogram is:
x = 4
Explanation:
The given quadrilateral would be a Parallelogram if the opposite sides of this quadrilateral are congruent.
As 3x + 2 and 5x - 6 are the opposite sides, so
5x - 6 = 3x + 2
subtracting 3x from both sides
5x - 6 - 3x = 3x + 2 - 3x
2x - 6 = 2
adding 6 to both sides
2x - 6 + 6 = 2 + 6
2x = 8
divide both sides by 2
2x/2 = 8/2
x = 4
Therefore, the value of x that makes the quadrilateral a parallelogram is:
x = 4
Verification:
5x - 6 = 5(4) - 6 = 20 - 6 = 14
3x + 2 = 3(4) + 2 = 12 + 2 = 14