Answer:
Step-by-step explanation:
To Determine:
Solve for x and find angle LMN.
Fetching Information and Solution Steps:
Considering the angle [tex]\angle{LMN}[/tex]
As MO bisects the angle [tex]\angle{LMN}[/tex] into two equal angle parts. These equal angles are:
[tex]\angle{LMO}=6x-22[/tex]
[tex]\angle{NMO}=2x+34[/tex]
As these angles are equal. i.e.
[tex]\angle{LMO}=\angle{NMO}[/tex]
[tex]6x-22=2x+34[/tex]
[tex]\mathrm{Add\:}22\mathrm{\:to\:both\:sides}[/tex]
[tex]6x-22+22=2x+34+22[/tex]
[tex]6x=2x+56[/tex]
[tex]\mathrm{Subtract\:}2x\mathrm{\:from\:both\:sides}[/tex]
[tex]6x-2x=2x+56-2x[/tex]
[tex]4x=56[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}4[/tex]
[tex]\frac{4x}{4}=\frac{56}{4}[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]x=14[/tex]
Hence, [tex]x=14[/tex]
As [tex]\angle{LMN}[/tex] was cut into two equal parts [tex]\angle{LMO}[/tex] and [tex]\angle{NMO}[/tex]
So,
[tex]\angle{LMN}[/tex] = [tex]\angle{LMO} + \angle{NMO}[/tex]
= [tex]6x-22+2x+34[/tex]
= [tex]8x + 12[/tex]
= [tex]8(14) + 12[/tex] ∵ [tex]x=14[/tex]
= [tex]124\textdegree[/tex]
Therefore, [tex]\angle{LMN}=124\textdegree[/tex]
Keywords: angle bisector, congruent angles
Learn more about angle bisector and congruent angles from brainly.com/question/711370
#learnwithBrainly
