Question

Which value of x would make Line segment N O is parallel to line segment K J?

Answer 1

Answer:

8

Step-by-step explanation:

I took the test

Answer 2

Answer:

x=8

Step-by-step explanation:

The picture of the question in the attached figure

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional

In this problem

If line segment NO is parallel to segment KJ

then

Triangle LNO is similar to Triangle LKJ by AA Similarity Theorem

so

$\frac{LN}{LK}=\frac{LO}{LJ}$

substitute the given values

$\frac{x-3}{2x-1}=\frac{x-4}{2x-4}$

solve for x

$(x-3)(2x-4)=(x-4)(2x-1)$

Apply distributive property

$2x^2-4x-6x+12=2x^2-x-8x+4$

Combine like terms

$2x^2-10x+12=2x^2-9x+4$

$10x-9x=12-4\\x=8$