Answer:
[tex]x=8\ in[/tex]
Step-by-step explanation:
we know that
If NO is parallel to KJ
then
Triangles LNO and LKJ are similar by AA Similarity Postulate
Remember that
If two figures are similar, then the ratio of its corresponding sides is equal
so
[tex]\frac{LO}{LJ}=\frac{LN}{LK}[/tex]
substitute the values
[tex]\frac{x-4}{x-4+x}=\frac{x-3}{x-3+x+2}[/tex]
[tex]\frac{x-4}{2x-4}=\frac{x-3}{2x-1}\\ \\(x-4)(2x-1)=(x-3)(2x-4)\\ \\2x^{2}-x-8x+4=2x^{2}-4x-6x+12\\ \\-9x+4=-10x+12\\ \\10x-9x=12-4\\ \\x=8\ in[/tex]
