Question

given that (mangle klh = 120^{circ}) and (mangle klm = 180^{circ}), which statement about the figure must be true? (angle hlm) is bisected by (overrightarrow{lj}). (mangle klg=mangle hlj) (angle glj) is bisected by (overrightarrow{lh}). (mangle hli = mangle ilm)

Explanation:

Step1: Calculate $\angle HLM$

$m\angle HLM=m\angle KLM - m\angle KLH=180^{\circ}-120^{\circ} = 60^{\circ}$

Step2: Analyze $\angle HLJ$

$m\angle HLJ = 30^{\circ}+15^{\circ}=45^{\circ}$, $m\angle KLG = 60^{\circ}$

Step3: Analyze angle - bisection

$m\angle HLI = 30^{\circ}$, $m\angle ILM=15^{\circ}$; $m\angle GLJ=60^{\circ}+30^{\circ}+15^{\circ}=105^{\circ}$, $m\angle GLH = 60^{\circ}$; $m\angle HLM = 60^{\circ}$, and since $m\angle HLJ=45^{\circ}
eq30^{\circ}$, $\overrightarrow{LJ}$ does not bisect $\angle HLM$.
$m\angle KLG = 60^{\circ}$, $m\angle HLJ=45^{\circ}$, so $m\angle KLG
eq m\angle HLJ$.
$m\angle GLJ = 105^{\circ}$, $m\angle GLH = 60^{\circ}$, so $\overrightarrow{LH}$ does not bisect $\angle GLJ$.
Since $m\angle HLI = 30^{\circ}$ and $m\angle ILM = 15^{\circ}$, $m\angle HLI
eq m\angle ILM$.

Answer:

None of the above statements are true.