Question

in the figure below, $m \angle jkm = 96^\circ$, $\overline{kl}$ bisects $\angle jkm$, and $\overline{kn}$ bisects $\angle lkm$. find $m \angle nkm$.
$m \angle nkm = \square^\circ$

Explanation:

Step1: Find m∠LKM

Since \( \overline{KL} \) bisects \( \angle JKM \), \( m\angle LKM = \frac{1}{2}m\angle JKM \). Given \( m\angle JKM = 96^\circ \), so \( m\angle LKM = \frac{96^\circ}{2} = 48^\circ \).

Step2: Find m∠NKM

Since \( \overline{KN} \) bisects \( \angle LKM \), \( m\angle NKM = \frac{1}{2}m\angle LKM \). Substituting \( m\angle LKM = 48^\circ \), we get \( m\angle NKM = \frac{48^\circ}{2} = 24^\circ \).

Answer:

\( 24 \)