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Number 10, please help

Number 10 Please Help class=

Sagot :

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].

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