Answer:
[tex]x=7,\\m\angle LKN = 84^{\circ}[/tex]
Step-by-step explanation:
1. For KM to be the angle bisector of angle LKN, it must be bisect LKN into two equal angles. Therefore, we have the following equation:
[tex]9x-21=6x,\\-21=-3x,\\x=\boxed{7}[/tex]
2. Substituting [tex]x=7[/tex]:
[tex]\angle LKN=9x-21+6x=9(7)-21+6(7)=63-21+42=\boxed{84^{\circ}}[/tex]
