Answer:
Choose one:
ray LG
ray LI
ray LJ
Step-by-step explanation:
There are three possible correct answers in this problem.
You only need one of them, but I will give you all three, and you choose the one you prefer.
Answer 1.
Ray LG is an angle bisector.
m<KLH = 120°
m<KLG + m<GLH = m<KLH
60° + m<GLH = 120°
m<GLH = 60°
Since m<KLG + m<GLH = m<KLH, and m<GLH = m<KLG, then
ray LG is the angle bisector of <KLH.
Answer: ray LG
Answer 2.
Angles KLH and HLM are a linear pair and supplementary. Their measures add to 180°. Since m<KLH = 120°, then m<HLM = 60°.
m<HLI = 30°, so m<ILM = 30°.
That makes ray LI a bisector of angle HLM.
Answer: ray LI
Answer 3.
Since ray LI bisects <HLM, and m<HLM = 60, then m<ILM = 30°.
We are given m<JLM = 15°, so m<ILJ is also 15°. That makes ray LJ an angle bisector.
Answer: ray LJ
