For the quadrilateral to be a parallelogram, x must be 20, and y must be 12.
For a quadrilateral to be a parallelogram, opposite sides must be equal. Therefore, we can set up two equations based on the opposite sides of the quadrilateral:
1. For sides AB and CD:
5x + 29 = 7x - 11
2. For sides AD and BC:
5y - 9 = 3y + 15
Let's solve these equations to find the values of x and y.
1. Equation 1:
5x + 29 = 7x - 11
2x = 40
x = 20
2. Equation 2:
5y - 9 = 3y + 15
2y = 24
y = 12
Therefore, for the quadrilateral to be a parallelogram, x must be 20, and y must be 12.