Question

$overleftrightarrow{h j}$ and $overleftrightarrow{k m}$ are parallel lines. which angles are alternate exterior angles? $angle j i g$ and $angle k l n$ $angle h i g$ and $angle k l i$ $angle k l i$ and $angle j i g$ $angle j i l$ and $angle h i l$

Explanation:

Step1: Recall the definition of alternate exterior angles

Alternate exterior angles are non - adjacent angles that lie outside the two parallel lines and on opposite sides of the transversal.

Step2: Analyze each option

• For \(\angle JIG\) and \(\angle KLN\):

\(\angle JIG\) and \(\angle KLN\) lie outside the parallel lines \(HJ\) and \(KM\) and on opposite sides of the transversal \(GN\).

• For \(\angle HIG\) and \(\angle KLI\): \(\angle HIG\) is outside, but \(\angle KLI\) is inside the parallel lines, so they are not alternate exterior angles.
• For \(\angle KLI\) and \(\angle JIG\): \(\angle KLI\) is inside the parallel lines, so they are not alternate exterior angles.
• For \(\angle JIL\) and \(\angle HIL\): These are adjacent angles (linear pair), not alternate exterior angles.

Answer:

\(\angle JIG\) and \(\angle KLN\)