Question

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

Explanation:

Step1: Analyze angle - measures

Given \(m\angle KLH = 120^{\circ}\), \(m\angle KLM=180^{\circ}\), and from the figure \(m\angle KLG = 60^{\circ}\), \(m\angle GLH = 60^{\circ}\), \(m\angle HLJ = 30^{\circ}\), \(m\angle JLM = 30^{\circ}\).

Step2: Check each option

For \(m\angle HLJ=m\angle JLM\), since \(m\angle HLJ = 30^{\circ}\) and \(m\angle JLM = 30^{\circ}\), this statement is true.

Answer:

\(m\angle HLJ = m\angle JLM\)