Question

which angles are alternate interior angles?
∠hgj and ∠fgj ∠fge and ∠kjg
∠hge and ∠jil ∠fgj and ∠kjg

Explanation:

Step1: Recall the definition of alternate interior angles

Alternate interior angles are non - adjacent angles that lie between two lines and on opposite sides of a transversal.

Step2: Analyze each option

• For \(\angle HGJ\) and \(\angle FGJ\): These are adjacent angles (share a common side \(GJ\)), so they are not alternate interior angles.
• For \(\angle FGE\) and \(\angle KJG\): \(\angle FGE\) is above line \(FH\) and \(\angle KJG\) is not in the correct position relative to the transversal \(EL\) and the lines \(FH\) and \(IK\) to be alternate interior angles.
• For \(\angle HGE\) and \(\angle IJL\): These are not between the two lines \(FH\) and \(IK\) in the correct way for alternate interior angles.
• For \(\angle FGJ\) and \(\angle KJG\):
• The lines \(FH\) and \(IK\) are cut by the transversal \(EL\).
• \(\angle FGJ\) and \(\angle KJG\) are non - adjacent, lie between \(FH\) and \(IK\), and are on opposite sides of the transversal \(EL\).

Answer:

\(\angle FGJ\) and \(\angle KJG\)