Question

in the figure below, m∠jkm = 109°, m∠lkm = 70°, and (overline{kn}) bisects ∠lkm. find m∠jkn.

Explanation:

Step1: Find angle JKL

Since $\angle JKM = 109^{\circ}$ and $\angle LKM=70^{\circ}$, we use the angle - difference formula. $\angle JKL=\angle JKM - \angle LKM$.
$m\angle JKL = 109^{\circ}-70^{\circ}=39^{\circ}$

Step2: Use the angle - bisector property

Since $\overline{KN}$ bisects $\angle LKM$, then $\angle LKN=\angle NKM$. And $m\angle LKN=\frac{m\angle LKM}{2}$. Given $m\angle LKM = 70^{\circ}$, so $m\angle LKN = 35^{\circ}$

Step3: Find angle JKN

$\angle JKN=\angle JKL+\angle LKN$.
$m\angle JKN=39^{\circ}+35^{\circ}=74^{\circ}$

Answer:

$74$