Question

given that m∠klh = 120° and m∠klm = 180°, which statement about the figure must be true? ∠hlm is bisected by lj. ∠glj is bisected by lh. m∠klg = m∠hlj m∠hli = m∠ilm

Explanation:

Step1: Calculate \(\angle HLM\)

Since \(m\angle KLM = 180^{\circ}\) and \(m\angle KLH=120^{\circ}\), then \(m\angle HLM=m\angle KLM - m\angle KLH=180 - 120=60^{\circ}\). There is no information to suggest \(\angle HLM\) is bisected by \(\overrightarrow{LJ}\).

Step2: Analyze \(\angle GLJ\)

There is no information given about the relationship between \(\angle GLJ\) and \(\overrightarrow{LH}\) to suggest bisection.

Step3: Calculate \(\angle KLG\) and \(\angle HLJ\)

\(m\angle KLG = 60^{\circ}\), \(m\angle HLJ=m\angle HLM - m\angle JLM=60 - 15 = 45^{\circ}\), so \(m\angle KLG
eq m\angle HLJ\).

Step4: Calculate \(\angle HLI\) and \(\angle ILM\)

\(m\angle HLI = 30^{\circ}\), \(m\angle ILM=30^{\circ}\), so \(m\angle HLI = m\angle ILM\).

Answer:

\(m\angle HLI = m\angle ILM\)