Question

select all the pairs of alternate interior angles. ∠kli and ∠jil ∠kln and ∠jig ∠jil and ∠jig ∠mli and ∠hil

Explanation:

Step1: Recall Alternate Interior Angles

Alternate interior angles are formed when a transversal crosses two parallel lines. They lie between the two lines (interior) and on opposite sides of the transversal.

Step2: Analyze Each Pair

• ∠KLI and ∠JIL: KL and HJ are parallel, LI is transversal. ∠KLI and ∠JIL are between KL, HJ (interior) and opposite sides of LI. So alternate interior.
• ∠KLN and ∠JIG: ∠KLN is exterior, ∠JIG is exterior? No, not interior. Eliminate.
• ∠JIL and ∠JIG: Same side of transversal, not alternate. Eliminate.
• ∠MLI and ∠HIL: ML (same as KL extended) and HI (same as HJ extended) are parallel, LI is transversal. ∠MLI and ∠HIL are between ML, HI (interior) and opposite sides of LI. So alternate interior.

Answer:

∠KLI and ∠JIL, ∠MLI and ∠HIL