Respuesta :

mhanifa

Answer:

  • D. x = 7 and m∠LMN = 120°

Step-by-step explanation:

Since MO bisect angle LMN, the angles formed are congruent:

  • ∠LMO≅∠NMO

Substitute values and solve for x:

  • 13x - 31 = x + 53
  • 13x - x = 53 + 31
  • 12x = 84
  • x = 7

Find the value of ∠LMN:

  • m∠LMN = 2*m∠LMO
  • m∠LMN = 2(13*7 - 31) = 120°

Correct option is D

Here,

MO is bisect of the [tex]\angle{LMN}[/tex],

SO,

[tex]\angle{LMO}[/tex]=~[tex]\angle{NMO}[/tex]

According to the question,

[tex]\bold{ 13x-31=x+53 }[/tex]

[tex]\bold{ 13x-x=53+31 }[/tex]

[tex]\bold{12x=84 }[/tex]

[tex]\bold{x=\dfrac{84}{12} }[/tex]

[tex]\bold{x=7 }[/tex]

Now we find the value of [tex]\angle{LMN }[/tex]

so,

[tex]\angle{LMO}=2×\angle{NMO }[/tex]

[tex]\bold{ 2×(13×7-37) }[/tex]

[tex]\bold{2×(91-31) }[/tex]

[tex]\bold{2×60 }[/tex]

[tex]\bold{120° }[/tex]

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