Question

Raj correctly determined that ray LH is the bisector of AngleGLI.

A line contains points K, L, M. 4 lines extend from point L. One line extends to point F, another to G, another to H, and another to I.
Which information could he have used to determine this?

AngleGLH Is-congruent-to AngleILM
mAngleKLM = 5mAngleILM
mAngleGLI = 2mAngleGLH
mAngleGLI = mAngleGLH + mAngleHLI

Answer 1

m∠GLI = 2·m∠GLH

Reason: Angle GLI is the sum of the two adjacent angles GLH and HLI, so
m∠GLI = m∠GLH + m∠HLI.
If m∠GLI = 2·m∠GLH, then 2·m∠GLH = m∠GLH + m∠HLI, hence m∠HLI = m∠GLH,
so LH divides ∠GLI into two congruent angles — LH is the bisector.