Question

I NEED HELP!! But it's not an emergency. 50 Points!!

Answer 1

Here,

MO is bisect of the
`\angle{LMN}`,

SO,

`\angle{LMO}`=~
`\angle{NMO}`

According to the question,

`\bold{ 13x-31=x+53 }`

`\bold{ 13x-x=53+31 }`

`\bold{12x=84 }`

`\bold{x=(84)/(12) }`

`\bold{x=7 }`

Now we find the value of
`\angle{LMN }`

so,

`\angle{LMO}=2×\angle{NMO }`

`\bold{ 2×(13×7-37) }`

`\bold{2×(91-31) }`

`\bold{2×60 }`

`\bold{120° }`

Answer 2

• D. x = 7 and m∠LMN = 120°

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