Question

in the figure below, ( m angle nkm = 26^{circ} ), ( overline{kl} ) bisects ( angle jkm ), and ( overline{kn} ) bisects ( angle lkm ). find ( m angle jkl ).

Explanation:

Step1: Analyze angle bisector of ∠LKM

Since \(\overline{KN}\) bisects \(\angle LKM\), we know that \(m\angle LKN = m\angle NKM\). Given \(m\angle NKM = 26^\circ\), so \(m\angle LKN = 26^\circ\), and then \(m\angle LKM=m\angle LKN + m\angle NKM=26^\circ + 26^\circ = 52^\circ\).

Step2: Analyze angle bisector of ∠JKM

Since \(\overline{KL}\) bisects \(\angle JKM\), we know that \(m\angle JKL=m\angle LKM\). From Step 1, we got \(m\angle LKM = 52^\circ\), so \(m\angle JKL = 52^\circ\).

Answer:

\(52\)