Question

in the figure below, m∠jkm = 108°, (overline{kl}) bisects ∠jkm, and (overline{kn}) bisects ∠lkm. find m∠nkm. m∠nkm = °

Explanation:

Step1: Find measure of ∠LKM

Since $\overline{KL}$ bisects $\angle JKM$ and $m\angle JKM = 108^{\circ}$, then $m\angle LKM=\frac{1}{2}m\angle JKM$.
$m\angle LKM=\frac{1}{2}\times108^{\circ} = 54^{\circ}$

Step2: Find measure of ∠NKM

Since $\overline{KN}$ bisects $\angle LKM$, then $m\angle NKM=\frac{1}{2}m\angle LKM$.
$m\angle NKM=\frac{1}{2}\times54^{\circ}=27^{\circ}$

Answer:

$27$