Erik draws quadrilateral ABCD If side AB=40x, side BC=4+3y side CD=8x+32, and side AD=9y−20, for what values of x and y can Erik be sure that his quadrilateral is a parallelogram?(1 point)
x=1 and y=4
x=20 and y=8
x=40 and y=16
x=4 and y=1
To determine if a quadrilateral is a parallelogram, we need to compare the opposite sides of the quadrilateral.
In this case, we need to compare sides AB and CD, as well as sides BC and AD.
For a quadrilateral to be a parallelogram, the opposite sides must be equal.
Comparing sides AB and CD:
AB = 40x
CD = 8x + 32
For AB and CD to be equal, we need to set up the following equation:
40x = 8x + 32
Simplifying the equation:
40x - 8x = 32
32x = 32
x = 1
Comparing sides BC and AD:
BC = 4 + 3y
AD = 9y - 20
For BC and AD to be equal, we need to set up the following equation:
4 + 3y = 9y - 20
Simplifying the equation:
3y - 9y = -20 - 4
-6y = -24
y = 4
Therefore, the values of x and y that make Erik's quadrilateral a parallelogram are:
x = 1 and y = 4
So the correct answer is:
x = 1 and y = 4