Question

which statement must be true about the diagram?○ point k is a midpoint of $overline{jl}$.○ $mangle jkn = \frac{1}{2}mangle jkm$○ ray km is an angle bisector of $angle nkl$.○ $jk = \frac{1}{2}kl$

Explanation:

Step1: Calculate ∠NKL

First, find $m\angle NKL$. Since $\overleftrightarrow{JL}$ is a straight line, $m\angle JKN + m\angle NKL = 180^\circ$.
$m\angle NKL = 180^\circ - 58^\circ = 122^\circ$

Step2: Check KM as angle bisector

Check if KM splits $\angle NKL$ into two equal angles. The diagram shows $m\angle NKM = 61^\circ$ and $m\angle MKL = 61^\circ$.
$\frac{1}{2}m\angle NKL = \frac{1}{2} \times 122^\circ = 61^\circ$, which equals $m\angle NKM$ and $m\angle MKL$.

Step3: Eliminate other options

• No info confirms K is midpoint of $\overline{JL}$, so first option is false.
• $m\angle JKN=58^\circ$, $\frac{1}{2}m\angle JKM=\frac{1}{2}(58+61+61)^\circ=90^\circ$, not equal, so second option is false.
• No info confirms $JK=\frac{1}{2}KL$, so fourth option is false.

Answer:

Ray KM is an angle bisector of ∠NKL.