Question

20 Pts + Brainliest for the best answer

Answer 1

Answer:

NMO = 59

Step-by-step explanation:

If MO bisects LMN  then LMO equals  OMN

LMN = LMO+OMN

Since LMO = OMN

LMN = LMO + LMO

LMN = 2 LMO

Substituting LMN = 5x-22 and LMO = x+31

5x - 22 = 2( x+31)

Distribute

5x-22 = 2x+62

Subtract 2x from each side

5x-2x-22 = 2x-2x+62

3x-22 = 62

Add 22 to each side

3x-22+22 =62+22

3x = 84

Divide by 3

3x/3 = 84/3

x =28

LMO = x+31

        =28+31

       =59

NMO = LMO

NMO = 59

Answer 2

If MO bisects ∠LMN then m∠LMO = m∠NMO

and m∠LMN = m∠LMO + m∠NMO

Therefore m∠LMN = 2 · m∠LMO

We have m∠LMN = 5x - 22 and m∠LMO = x + 31. Substitute:

5x - 22 = 2(x + 31)        use distributive property a(b + c) = ab + ac

5x - 22 = (2)(x) + (2)(31)

5x - 22 = 2x + 62        add 22 to both sides

5x = 2x + 84         subtract 2x from both sides

3x = 84       divide both sides by 3

x = 28

m∠NMO = m∠LMO = x + 31

Put the value of x:

m∠NMO = 28 + 31 = 59

Answer: m∠NMO = 59°