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The figure is quadrilateral L M N O. It appears to be a parallelogram.
If ON = 8x − 8,
LM = 7x + 4, NM = x − 5,
and OL = 3y − 6,
find the values of x and y for which LMNO must be a parallelogram. The diagram is not drawn to scale.
(2 points)
To determine the values of x and y for which LMNO must be a parallelogram, we need to use the properties of parallelograms.
In a parallelogram, opposite sides are equal in length. Therefore, we can set the lengths of the opposite sides in the figure equal to each other and solve for x and y.
ON = LM (opposite sides are equal in length)
8x - 8 = 7x + 4
Simplifying the equation, we have:
8x - 7x = 4 + 8
x = 12
OL = NM (opposite sides are equal in length)
3y - 6 = x - 5
Substituting the value of x we found above, we have:
3y - 6 = 12 - 5
3y - 6 = 7
Adding 6 to both sides of the equation, we have:
3y = 13
Dividing both sides of the equation by 3, we have:
y = 13/3
Therefore, the values of x and y for which LMNO must be a parallelogram are x = 12 and y = 13/3.