LO bisects∠NLM, LM=26, NO=8, and LN=18. What is the value of x?

Answer: 11.56

Step-by-step explanation:

LO bisects∠NLM,

LM=26, NO=8 and LN=18

We will use the angle bisector theorem

When a line bisects an angle, ratio of the two connecting sides with the angle that is bisected will be equal to the ratio of length of the segments whereby the angle bisector intersects the third side.

LN/LM = NO/OM

Let OM be represented by x

18/26 = 8/x

Cross multiply

18 * x = 26 * 8

18x = 208

x = 208/18

x = 11.56

OM = 11.56