Question

fh and ik are parallel lines. which angles are alternate exterior angles? ∠ijl and ∠hge ∠ijl and ∠kjl ∠ijl and ∠hgj ∠ijl and ∠fge

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 \(\angle IJL\) and \(\angle HGE\): \(\angle HGE\) is not related to the parallel lines \(FH\) and \(IK\) in the correct position for alternate exterior angles with \(\angle IJL\).
• For \(\angle IJL\) and \(\angle KJL\): These are adjacent angles, not alternate exterior angles.
• For \(\angle IJL\) and \(\angle HGJ\): \(\angle HGJ\) is not in the correct position (not outside the parallel lines in the right relation) to be an alternate exterior angle with \(\angle IJL\).
• For \(\angle IJL\) and \(\angle FGE\): \(\angle IJL\) and \(\angle FGE\) are non - adjacent, lie outside the parallel lines \(FH\) and \(IK\), and are on opposite sides of the transversal \(EL\).

Answer:

\(\angle IJL\) and \(\angle FGE\)