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 ).

Explanation:

Step1: Find m∠LKM

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

Step2: Find m∠NKM

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

Answer:

\( 24 \)