Question

in the figure below, ( mangle jkm = 82^{circ}, mangle lkm = 52^{circ} ), and ( overline{kn} ) bisects ( angle lkm ). find ( mangle jkn ).

Explanation:

Step1: Find the measure of ∠LKN

Since \( \overline{KN} \) bisects \( \angle LKM \), by the angle - bisector definition, \( m\angle LKN=\frac{1}{2}m\angle LKM \).
Given \( m\angle LKM = 52^{\circ} \), then \( m\angle LKN=\frac{1}{2}\times52^{\circ}=26^{\circ} \).

Step2: Find the measure of ∠JKN

By the angle - addition postulate, \( m\angle JKN=m\angle JKM - m\angle LKN \).
Given \( m\angle JKM = 82^{\circ} \) and \( m\angle LKN = 26^{\circ} \), then \( m\angle JKN=82^{\circ}-26^{\circ}=56^{\circ} \).

Answer:

\(56\)