Question

If ON = 7x - 7, LM = 6x + 3, NM = x - 6, and OL = 4y + 5, find the values of x and y given that LMNO is a parallelogram.

Options:
A) x = 5, y = 3
B) x = 8, y = 2
C) x = 6, y = 4
D) x = 10, y = 1

Answer 1

To find the values of x and y in the parallelogram LMNO, we can use the properties of parallel lines. By setting up equations for the opposite sides of the parallelogram and solving, we find x = 10 and y = 1.

Step-by-step explanation:

To find the values of x and y, we need to use the properties of parallel lines in a parallelogram.

Since LMNO is a parallelogram, opposite sides are equal in length.

Using the given information, we have:

• ON = 7x - 7
• LM = 6x + 3
• NM = x - 6
• OL = 4y + 5

From the properties of a parallelogram, we know that ON = LM and NM = OL.

Setting up these equations, we get:

• 7x - 7 = 6x + 3
• x - 6 = 4y + 5

Solving these equations, we find x = 10 and y = 1. Therefore, the correct option is D) x = 10, y = 1.