Question

LO bisects∠NLM, LM=18, NO=4, and LN=10. What is the value of x?

Answer 1

Solution:

→LO bisects∠NLM,

→LM=18, NO=4, and LN=10.

Use angle bisector theorem

If a line bisects an angle, the ratio of two connecting sides with that angle which is bisected,is equal to ratio of the length of segments where the angle bisector is intersecting the third side.

$\frac{NL}{LM}=\frac{NO}{OM}\\\\ \frac{10}{18}=\frac{4}{x}\\\\ 10 x=72 \\\\ x=7.2$

OM=x=7.2 units