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°
