Question

in the figure below, $m\angle jkm = 78^\circ$, $m\angle lkm = 42^\circ$, and $\overline{kn}$ bisects $\angle lkm$. find $m\angle jkn$.
$m\angle jkn = \square ^\circ$

Explanation:

Step1: Find measure of ∠LKN

Since \( \overline{KN} \) bisects \( \angle LKM \), \( m\angle LKN=\frac{1}{2}m\angle LKM \). Given \( m\angle LKM = 42^\circ \), so \( m\angle LKN=\frac{42^\circ}{2}=21^\circ \).

Step2: Find measure of ∠JKN

We know \( m\angle JKM = 78^\circ \) and \( m\angle LKM = 42^\circ \), first find \( m\angle JKL=m\angle JKM - m\angle LKM=78^\circ - 42^\circ = 36^\circ \). Then \( m\angle JKN=m\angle JKL + m\angle LKN=36^\circ+21^\circ = 57^\circ \).

Answer:

\( 57 \)