Question

given that m∠klh = 120° and m∠klm = 180°, which statement about the figure must be true? ∠hlm is bisected by (overrightarrow{li}) ∠glj is bisected by (overrightarrow{lh}) m∠klg = m∠hlj m∠hlj = m∠ilm

Explanation:

Step1: Calculate $m\angle GLH$

Since $m\angle KLH = 120^{\circ}$ and the angle adjacent to $\angle KLG$ within $\angle KLH$ is $60^{\circ}$, then $m\angle GLH=120 - 60=60^{\circ}$.

Step2: Calculate $m\angle HLJ$

We know that the sum of angles in the figure around point $L$ is based on the straight - line $\angle KLM = 180^{\circ}$. Given the other angles, $m\angle HLJ=180-(60 + 30+15)- 75=60^{\circ}$.

Step3: Compare angles

Since $m\angle KLG = 60^{\circ}$ and $m\angle HLJ = 60^{\circ}$, we have $m\angle KLG=m\angle HLJ$.

Answer:

C. $m\angle KLG=m\angle HLJ$