Question

X = ____

m∠LMN = ____
I cant really figure out how you find X. If someone could help it would be much appreciated.

Answer 1

The clue is in the first sentence. MO bisects LMN. This means that LMN is split into two equal halves: LMO and NMO.

LMO = NMO
7x - 29 = 2x + 31
7x - 29 + 29 = 2x + 31 + 29
7x = 2x + 60
7x - 2x = 2x - 2x + 60
5x = 60
5x/5 = 60/5
x = 12

We now know the value of x, and can solve for anything that involves x. We need to find LMN.

LMN = LMO + NMO
LMN = 7x - 29 + 2x + 31
LMN = 9x + 2
LMN = 9(12) + 2
LMN = 108 + 2
LMN = 110

Answer 2

since you know it bisects < LMN,
Therefore you can set the equations equal to each other to find x= 12

plug that back into either equation
ex. 2(12)+31= 55

since that is only the value of one angle, you must multiply that value by 2 to find the big angle and get 110


LMN is 110