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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.

Respuesta :

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.

[tex]7x + 4 = 8x - 8[/tex]

[tex]7x - 8x = - 8 - 4[/tex]

[tex] - x = - 12[/tex]

[tex] \boxed{x = 12}[/tex]

Now, let us find y, in same way.

[tex]x - 9 = 5y - 7[/tex]

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

[tex]12 - 9 = 5y - 7[/tex]

[tex]3 = 5y - 7[/tex]

[tex]3 + 7 = 5y[/tex]

[tex]10 = 5y[/tex]

[tex] \boxed{y = \frac{10}{5} = 2}[/tex]

So value of y is 2.

If viewing in Brainly app, extend [tex]\longrightarrow[/tex] side.

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