Question

in the figure below, m∠jkm = 92°, kt bisects ∠jkm, and kn bisects ∠lkm. find m∠nkm.

Explanation:

Step1: Find measure of ∠LKM

Since $\overrightarrow{KT}$ bisects $\angle{JKM}$ and $m\angle{JKM}=92^{\circ}$, then $m\angle{LKM}=\frac{1}{2}m\angle{JKM}$. So $m\angle{LKM}=\frac{1}{2}\times92^{\circ} = 46^{\circ}$.

Step2: Find measure of ∠NKM

Since $\overrightarrow{KN}$ bisects $\angle{LKM}$, then $m\angle{NKM}=\frac{1}{2}m\angle{LKM}$. Substituting the value of $m\angle{LKM}=46^{\circ}$, we get $m\angle{NKM}=\frac{1}{2}\times46^{\circ}=23^{\circ}$.

Answer:

$23$