Question

in the figure below, ( mangle nkm = 24^{circ} ), ( overline{kl} ) bisects ( angle jkm ), and ( overline{kn} ) bisects ( angle lkm ). find ( mangle jkl ).

Explanation:

Step1: Find \( m\angle LKM \)

Since \( \overline{KN} \) bisects \( \angle LKM \), then \( m\angle LKM = 2\times m\angle NKM \).
Given \( m\angle NKM = 24^{\circ} \), so \( m\angle LKM=2\times24^{\circ}=48^{\circ} \).

Step2: Find \( m\angle JKL \)

Since \( \overline{KL} \) bisects \( \angle JKM \), then \( m\angle JKL = m\angle LKM \).
So \( m\angle JKL = 48^{\circ} \).

Answer:

\(48\)