Question

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

Explanation:

Step1: Recall angle - bisector property

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

Step2: Use angle - bisector property again

Since $\overline{KL}$ bisects $\angle JKM$, then $m\angle JKL=m\angle LKM$.

Answer:

$52$