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:

Step1: Recall the angle - bisector definition

An angle bisector divides an angle into two equal - measure angles. If \(LH\) is the bisector of \(\angle GLH\), then \(m\angle GLH=m\angle HLH\).

Step2: Analyze the angle - addition postulate

The angle - addition postulate states that if we have an angle \(\angle GLI\) which is composed of \(\angle GLH\) and \(\angle HLI\), then \(m\angle GLI = m\angle GLH+m\angle HLI\).

Answer:

\(m\angle GLI=\frac{1}{2}m\angle GLH+\frac{1}{2}m\angle HLI\)