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 the measure of ∠NKL. Since JL is a straight line, ∠JKL = 180°. We know ∠JKN = 58°, so:
$$m\angle NKL = 180^\circ - 58^\circ = 122^\circ$$

Step2: Check KM as angle bisector

We are given ∠MKL = 61°. Calculate twice this measure:
$$2 \times 61^\circ = 122^\circ$$
This equals the measure of ∠NKL, so KM splits ∠NKL into two equal angles.

Step3: Eliminate other options

• No information confirms K is the midpoint of $\overline{JL}$ or $JK = \frac{1}{2}KL$.
• Calculate $m\angle JKM = 58^\circ + 61^\circ + 61^\circ = 180^\circ$, so $\frac{1}{2}m\angle JKM = 90^\circ$, which does not equal $m\angle JKN = 58^\circ$.

Answer:

Ray KM is an angle bisector of ∠NKL.