Question

2025 geometry fall measuring length and angles given that m∠klh = 120° and m∠klm = 180°, which statement about the figure must be true? m∠klg = m∠hlj ∠glj is bisected by lh. ∠hlm is bisected by lj.

Explanation:

Step1: Calculate \(m\angle KLG\)

Since \(m\angle KLM = 180^{\circ}\) and \(m\angle KLG+ m\angle GLM=180^{\circ}\), and \(m\angle GLM = 60^{\circ}\), then \(m\angle KLG=180 - 60=60^{\circ}\).

Step2: Calculate \(m\angle HLJ\)

We know \(m\angle KLH = 120^{\circ}\), and \(m\angle KLH=m\angle KLG + m\angle GLH\), so \(m\angle GLH = 120 - 60 = 60^{\circ}\). Also, \(m\angle GLH+m\angle HLJ+m\angle JLM=180^{\circ}\), and \(m\angle JLM = 15^{\circ}\), \(m\angle GLH = 60^{\circ}\), then \(m\angle HLJ=180-(60 + 15)=105 - 15=60^{\circ}\).

Answer:

\(m\angle KLG = m\angle HLJ\)