Answer: The required value of x is 14 and the maesure of angle LMN is 128 degrees.
Step-by-step explanation: As given in the question and shown in the attached figure below, ray MO bisects angle LMN.
Also,
[tex]m\angle LMO=6x-20,\\\\m\angle NMO=2x+36.[/tex]
We are to find the value of x and the measure of angle LMN.
Since ray MO bisects angle LMN, so we must have
[tex]m\angle LMO=m\angle NMO\\\\\Rightarrow 6x-20=2x+36\\\\\Rightarrow 6x-2x=36+20\\\\\Rightarrow 4x=56\\\\\Rightarrow x=\dfrac{56}{4}\\\\\Rightarrow x=14.[/tex]
And, we get
[tex]m\angle LMN=6x-20+2x+36=8x+16=8\times14+16=112+16=128.[/tex]
Thus, the required value of x is 14 and the maesure of angle LMN is 128 degrees.
