Question

If ON = 8x − 8, LM = 7x + 4, NM = x − 9, and OL = 5y − 7, find the values of x and y for which LMNO must be a parallelogram.

Answer 1

Step-by-step explanation:

Answer:-

Given :-

• ON = 8x − 8
• LM = 7x + 4
• NM = x − 9
• OL = 5y − 7

We need to find the value if x and y.

Concept:-

The sides of a parallelogram, where equal and where they are not.

Working with it:-

If LMNO is a parallelogram, the sides LM is opposite ON.

$7x + 4 = 8x - 8$

$7x - 8x = - 8 - 4$

$- x = - 12$

$\boxed{x = 12}$

Now, let us find y, in same way.

$x - 9 = 5y - 7$

Now, we found the value of x as 12, we will place it.

$12 - 9 = 5y - 7$

$3 = 5y - 7$

$3 + 7 = 5y$

$10 = 5y$

$\boxed{y = \frac{10}{5} = 2}$

So value of y is 2.

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