Answer: x= 8
Step-by-step explanation:
According to the converse of basic proportionality theorem,
If in ΔABC , DE is a line drawn from AB to AC such that [tex]\dfrac{AD}{DB}=\dfrac{AE}{EB}[/tex]
then, DE is parallel to the third side BC.
Applying converse of basic proportionality theorem, to get NO parallel to KJ, we must have
[tex]\dfrac{LO}{OJ}=\dfrac{LN}{NK}\\\\\Rightarrow \dfrac{x-4}{x}=\dfrac{x-3}{x+2}\\\\\Rightarrow\ (x-4)(x+2)=x(x-3)\\\\\Rightarrow\ x^2-2x-8=x^2-3x\\\\\Rightarrow\ -2x+3x=8\\\\\Rightarrow\ x=8[/tex]
Hence, the value of x should be 8, so that Line segment N O is parallel to line segment K J.
