Question

which angles are alternate interior angles? ∠hil and ∠mli ∠kln and ∠jig ∠hig and ∠hil ∠mln and ∠hig

Explanation:

Step1: Recall alternate - interior angles definition

Alternate - interior angles are formed when a transversal intersects two lines. They are on the interior of the two lines and on opposite sides of the transversal.

Step2: Analyze each option

For the pair ∠HIL and ∠MLI: They are between the two lines (formed by the rays with endpoints H and M) and on opposite sides of the transversal (the line NLG).
For ∠KLN and ∠JIG: ∠KLN is not an interior - angle formed by the intersection of the relevant lines and transversal.
For ∠HIG and ∠HIL: They are adjacent angles, not alternate - interior angles.
For ∠MLN and ∠HIG: ∠MLN is not an interior - angle in the context of the two lines and transversal for the relevant angle - pair relationship.

Answer:

∠HIL and ∠MLI