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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?
To find the value of x, we can use the Angle Bisector Theorem.
The Angle Bisector Theorem states that in a triangle, a line segment that bisects an angle will divide the opposite side into two segments that are proportional to the other two sides.
In this case, the angle bisector LO divides side MN into two segments.
Let's label the length of the segment x as y.
Using the Angle Bisector Theorem, we have:
LM/LN = MO/NO
Substituting the given values:
18/10 = y/4
Cross multiplying:
18 * 4 = 10 * y
72 = 10y
Dividing both sides by 10:
y = 7.2
Therefore, the value of x is 7.2.