Answer:
A quadrilateral is a parallelogram if and only if opposite angles are equal.
So, to make the quadrilateral a parallelogram, we can set the following equalities:
(4x + 13) deg = (5x - 12) deg
(4y + 7) deg = (3x - 8) deg
Solving the first equation,
4x + 13 = 5x - 12
x = -5
Solving the second equation,
4y + 7 = 3(-5) - 8
4y + 7 = -17
4y = -24
y = -6
So, the values of x and y that make the quadrilateral a parallelogram are x = -5 and y = -6