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.

Question

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

Answer 1

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.