Answer:
[tex]m\angle{JKN}=82^{\circ}[/tex]
Step-by-step explanation:
Since [tex]\overline{KN}[/tex] bisects [tex]\angle{LKM}[/tex], it follows:
[tex]m\angle{NKL}=m\angle{NKM}[/tex].
It is given that [tex]m\angle{NKL}=7x-9[/tex] so it holds [tex]m\angle{NKM}=7x-9[/tex].
By using Angle Addition Postulate:
[tex]m\angle{JKM}+m\angle{NKM}+m\angle{LKN}=m\angle{JKL}[/tex]
Since [tex]m\angle{JKL}=180^{\circ}[/tex], substitute all the measures of the angles:
[tex](x+3)^{\circ}+(7x-9)^{\circ}+(7x-9)^{\circ}=180^{\circ}[/tex]
Simplify:
[tex](15x-15)^{\circ}=180^{\circ}[/tex]
Solve the equation by [tex]x[/tex]:
[tex]15x=180-15[/tex]
[tex]15x=165[/tex]
[tex]x=165\div 15[/tex]
[tex]x=11[/tex]
Notice that:
[tex]m\angle{JKN}=m\angle{JKM}+m\angle{NKM}=(x+3)+(7x-9)[/tex]
Substitute [tex]x=11[/tex] into the equation:
[tex]m\angle{JKN}=(11+3)+(7\cdot 11-9)=14+(77-9)=14+68=82[/tex]
Therefore, [tex]m\angle{JKN}=82^{\circ}[/tex].
