Question

in the figure below, (mangle{jkm}=89^{circ}, mangle{nkm}=21^{circ}), and (overline{kn}) bisects (angle{lkm}). find (mangle{jkl}).

Explanation:

Step1: Find $m\angle LKM$

Since $\overline{KN}$ bisects $\angle LKM$ and $m\angle NKM = 21^{\circ}$, then $m\angle LKM=2\times m\angle NKM$. So $m\angle LKM = 2\times21^{\circ}=42^{\circ}$.

Step2: Find $m\angle JKL$

We know that $m\angle JKM=m\angle JKL + m\angle LKM$. So $m\angle JKL=m\angle JKM - m\angle LKM$. Given $m\angle JKM = 89^{\circ}$ and $m\angle LKM = 42^{\circ}$, then $m\angle JKL=89^{\circ}- 42^{\circ}=47^{\circ}$.

Answer:

$47$