Modifying above upper M upper O with right-arrowbisects angle upper L upper M upper N, mangle upper L upper M upper N = 6x – 28, mangle upper L upper M upper O = x + 34. Find mangle upper N upper M upper O. The diagram is not to scale.
Angle upper L upper M upper N is shown. Point upper O lies in the interior of the angle between upper L and upper N. Ray upper M upper O is drawn.
(1 point)
Responses
46.4
46.4
92.8
92.8
63
63
58
We can set up an equation using the information given:
m∠LMN = 6x - 28 (angle LMN)
m∠LMO = x + 34 (angle LMO)
Since MO bisects angle LMN, we know that m∠LMO is equal to m∠NMO. We can set these two angles equal to each other:
x + 34 = 6x - 28
Solving for x:
34 + 28 = 6x - x
62 = 5x
x = 12.4
Now we can substitute this value of x back into the equation for m∠NMO:
m∠NMO = 6x - 28 = 6(12.4) - 28 = 74.4 - 28 = 46.4
Therefore, m∠NMO = 46.4.