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 = \frac{1}{2}m∠glh + \frac{1}{2}m∠hli

Explanation:

An angle bisector divides an angle into two equal parts. If \(LH\) is the bisector of \(\angle GLI\), then \(m\angle GLH=m\angle HLI\) and \(m\angle GLI = m\angle GLH+m\angle HLI\). Substituting \(m\angle HLI=m\angle GLH\) into the second equation gives \(m\angle GLI = 2m\angle GLH\).

• For \(\angle GLH\cong\angle ILM\), these angles are not related to the bisecting of \(\angle GLI\) as they are not adjacent angles formed by the bisector of \(\angle GLI\).
• For \(m\angle KLM = 5m\angle ILM\), \(\angle KLM\) is a straight - angle (\(m\angle KLM = 180^{\circ}\)) and this relation has no direct connection to the bisecting of \(\angle GLI\).
• For \(m\angle GLI=\frac{1}{2}m\angle GLH+\frac{1}{2}m\angle HLI\), if \(LH\) is the bisector \(m\angle GLH = m\angle HLI\), then \(m\angle GLI=m\angle GLH + m\angle HLI=2m\angle GLH\) (not the given formula).

Answer:

\(m\angle GLI = 2m\angle GLH\)