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: Use the angle - bisector property for \(\overline{KN}\)

Since \(\overline{KN}\) bisects \(\angle LKM\), then \(m\angle LKN=m\angle NKM\). Given \(m\angle NKM = 24^{\circ}\), so \(m\angle LKN = 24^{\circ}\). Then \(m\angle LKM=m\angle LKN + m\angle NKM=24^{\circ}+24^{\circ}=48^{\circ}\).

Step2: Use the angle - bisector property for \(\overline{KL}\)

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

Answer:

\(48\)