Question

1. in the figure, m∠jkm = 93°, m∠nkm = 23°, and (overline{kn}) bisects ∠lkm. find m∠jkl. (1pt)

(a) m∠jkl = ______

Explanation:

Step1: Find m∠LKN

Since $\overline{KN}$ bisects $\angle LKM$ and $m\angle NKM = 23^{\circ}$, then $m\angle LKN=m\angle NKM = 23^{\circ}$ (by the definition of angle - bisector).

Step2: Find m∠JKL

We know that $m\angle JKM=93^{\circ}$ and $m\angle JKL + m\angle LKM=m\angle JKM$. Also, $m\angle LKM = 2\times m\angle NKM=46^{\circ}$. So, $m\angle JKL=m\angle JKM - m\angle LKM$. Substituting the values, we get $m\angle JKL=93^{\circ}- 46^{\circ}=47^{\circ}$.

Answer:

$47$