Question

Ray MO bisects LMN LMO = 6x-20 and NMO =2x+36. solve for x and find LMN

Answer 1

6x - 20 = 2x + 36
6x - 2x = 36 + 20
4x = 56
x = 56/4
x = 14

m∠LMN = 6x - 20 + 2x + 36 = 8x + 16 = 8 * 14 + 16 = 128°

Answer 2

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,

$m\angle LMO=6x-20,\\\\m\angle NMO=2x+36.$

We are to find the value of x and the measure of angle LMN.

Since ray MO bisects angle LMN, so we must have

$m\angle LMO=m\angle NMO\\\\\Rightarrow 6x-20=2x+36\\\\\Rightarrow 6x-2x=36+20\\\\\Rightarrow 4x=56\\\\\Rightarrow x=\dfrac{56}{4}\\\\\Rightarrow x=14.$

And, we get

$m\angle LMN=6x-20+2x+36=8x+16=8\times14+16=112+16=128.$

Thus, the required  value of x is 14 and the maesure of angle LMN is 128 degrees.