Question

in the figure below, (mangle jkm = 105^{circ},mangle nkm = 28^{circ}), and (overline{kn}) bisects (angle lkm). find (mangle jkl).

Explanation:

Step1: Find m∠LKM

Since $\overline{KN}$ bisects $\angle LKM$ and $m\angle NKM = 28^{\circ}$, then $m\angle LKM=2\times m\angle NKM$.
$m\angle LKM = 2\times28^{\circ}=56^{\circ}$

Step2: Find m∠JKL

We know that $m\angle JKM=m\angle JKL + m\angle LKM$. So, $m\angle JKL=m\angle JKM - m\angle LKM$.
Given $m\angle JKM = 105^{\circ}$ and $m\angle LKM = 56^{\circ}$, then $m\angle JKL=105^{\circ}- 56^{\circ}=49^{\circ}$

Answer:

$49$