Answer:
Step-by-step explanation:
From the given figure, we have
[tex]KN=NM[/tex]
⇒[tex]14x-3=25[/tex]
⇒[tex]14x=28[/tex]
⇒[tex]x=2[/tex]
Also, a is the angle bisector of ∠KNM and also it bisects the side KM such that KL=LM, thus
[tex]KL=LM[/tex]
Also, [tex]KL=9x+5[/tex]
Substituting the value of x in the above equation, we get
[tex]KL=9(2)+5[/tex]
[tex]KL=18+5[/tex]
[tex]KL=23[/tex]
Therefore, [tex]KL=LM[/tex]
[tex]LM=23[/tex]
Thus, the value of the segment LM is 23.
