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Triangle N L M is shown with an angle bisector from vertex L through point O on side N M.Segment O M is labeled x.
LO−→
bisects ∠NLM
, LM = 18, NO = 4, and LN = 10. What is the value of x?
(2 points)
First, we can use the angle bisector theorem to find the ratio of NO to OM. The angle bisector theorem states that the ratio of the lengths of the segments formed by an angle bisector is equal to the ratio of the lengths of the sides opposite those segments. In this case, since LO is the angle bisector, the ratio of NO to OM is equal to the ratio of LN to LM.
Therefore, we have:
NO/OM = LN/LM
Substituting the given values, we have:
4/OM = 10/18
Now, we can cross-multiply:
10*OM = 4*18
Simplifying, we get:
10*OM = 72
Dividing both sides by 10, we find:
OM = 7.2
So the value of x, which is equal to OM, is 7.2.