Let's find the value of each variable one at a time.
Value of x
Recall the Theorem 6.11, which tells us that if the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
Therefore, the segments with lengths x + 4 and 3x - 6 must be congruent. By the definition of congruent segments, their lengths must be equal.
x + 4 = 3x - 6
Let's solve this equation.
Notice that 5y and 60 are alternate interior angles. Opposite sides of the quadrilateral must be parallel, so that it is a parallelogram. Therefore 5y and 60 must be equal.
5y = 60 ⇔ y = 12
