Question

raj correctly determined that ray lh is the bisector of ∠gli. which information could he have used to determine this? ∠glh ≅ ∠ilm m∠klm = 5m∠ilm m∠gli = 2m∠glh m∠gli = 1/2m∠glh + 1/2m∠hli

Explanation:

Step1: Recall the angle - bisector definition

An angle bisector divides an angle into two equal - measure angles. If \(LH\) is the bisector of \(\angle GLI\), then \(\angle GLH=\angle HLI\) and \(m\angle GLI = m\angle GLH + m\angle HLI\). Since \(\angle GLH=\angle HLI\), we can substitute \(m\angle HLI\) with \(m\angle GLH\).

Step2: Simplify the angle - sum formula

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• For \(\angle GLH\cong\angle ILM\): There is no relation between \(\angle GLH\) and \(\angle ILM\) based on the angle - bisector of \(\angle GLI\) definition.
• For \(m\angle KLM = 5m\angle ILM\): \(\angle KLM\) is a straight - angle (\(m\angle KLM = 180^{\circ}\)) in this case (assuming \(KLM\) is a straight line). This has no direct relation to the bisector of \(\angle GLI\).
• For \(m\angle GLI=\frac{1}{2}m\angle GLH+\frac{1}{2}m\angle HLI\): If \(LH\) is the bisector, \(m\angle GLI=m\angle GLH + m\angle HLI = 2m\angle GLH\) (not the given formula).

Answer:

\(m\angle GLI = 2m\angle GLH\) (the third option)