Question

in the figure below, (mangle jkm = 96^{circ}), (mangle nkm = 26^{circ}), and (overline{kn}) bisects (angle lkm). find (mangle jkl).

Explanation:

Step1: Find m∠LKM

Since $\overline{KN}$ bisects $\angle LKM$ and $m\angle NKM = 26^{\circ}$, then $m\angle LKM=2\times m\angle NKM$.
$m\angle LKM = 2\times26^{\circ}=52^{\circ}$

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 $m\angle JKM = 96^{\circ}$ and $m\angle LKM = 52^{\circ}$, then $m\angle JKL=96^{\circ}-52^{\circ}=44^{\circ}$

Answer:

$44$