Question

in the figure below, (mangle jkm = 107^{circ},mangle lkm = 66^{circ}), and (overline{kn}) bisects (angle lkm). find (mangle jkn). (mangle jkn=square^{circ})

Explanation:

Step1: Find the measure of ∠LKN

Since $\overline{KN}$ bisects $\angle LKM$ and $m\angle LKM = 66^{\circ}$, then $m\angle LKN=\frac{1}{2}m\angle LKM$. So $m\angle LKN=\frac{66^{\circ}}{2}=33^{\circ}$.

Step2: Find the measure of ∠JKN

We know that $m\angle JKN=m\angle JKM - m\angle LKM+ m\angle LKN$. Substitute $m\angle JKM = 107^{\circ}$ and $m\angle LKM = 66^{\circ}$ and $m\angle LKN = 33^{\circ}$ into the formula. $m\angle JKN=107^{\circ}-66^{\circ}+33^{\circ}$. First, $107 - 66=41^{\circ}$, then $41^{\circ}+33^{\circ}=74^{\circ}$.

Answer:

$74$