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In parallelogram DEFG, DH = x + 1, HF = 3y, GH = 3x − 4,
and HE = 5y + 1. Find the values of x and y.
Since we know that DEFG is a parallelogram, we can use the properties of parallelogram to find the values of x and y.
One property of parallelograms is that opposite sides are equal in length. Therefore, we can set up the following equations:
DH = FG (opposite sides of parallelogram are equal)
x + 1 = 3x - 4 (substituting the given values)
4 = 2x
x = 2
HF = EG (opposite sides of parallelogram are equal)
3y = 5y + 1 (substituting the given values)
-2y = 1
y = -1/2
Therefore, the values of x and y are x = 2 and y = -1/2.