which statement must be true about the diagram? point k is a mid - point of jl. m∠jkn = 1/2m∠jkm ray km is…

Answer:

B. $m\angle{JKN}=\frac{1}{2}m\angle{JKM}$

Explanation:

Step1: Analyze angle - measures

We know that $\angle{JKN} = 58^{\circ}$ and $\angle{JKM}=58^{\circ}+61^{\circ}=119^{\circ}\approx2\times58^{\circ}$.

Step2: Check mid - point condition

There is no indication that $K$ is the mid - point of $\overline{JL}$ as no length information about $\overline{JK}$ and $\overline{KL}$ is given to suggest $JK = KL$.

Step3: Check angle - bisector for $\angle{NKL}$

$\angle{NKL}=58^{\circ}+61^{\circ}=119^{\circ}$, and since $\angle{MKL}=61^{\circ}$ and $\angle{NKL}\neq2\angle{MKL}$, ray $KM$ is not the angle - bisector of $\angle{NKL}$.

Step4: Check length relation

No length information is given to suggest that $JK=\frac{1}{2}KL$.