Answer:
x=8
Step-by-step explanation:
The figure is shown in the attached figure.
We have, LK║OM. We need to find the value of x.
It is based on side-splitter theorem. If a line is parallel to third side of a triangle, then the points that intersects the two lines, it divides proportionally.
Using it in given problem. So,
[tex]\dfrac{\text{NK}}{\text{KM}}=\dfrac{\text{NL}}{\text{LO}}[/tex]
Nk = x+2, KM = x-3, NL = x and LO = x-4
So,
[tex]\dfrac{x+2}{x-3}=\dfrac{x}{x-4}[/tex]
Cross multiplying, we get :
[tex](x+2)(x-4)=x(x-3)\\\\x^2-4x+2x-8=x^2-3x\\\\-2x+3x=8\\\\x=8[/tex]
So, the value of x is 8.
