Question

fh and ik are parallel lines. which angles are vertical angles? ∠fge and ∠kjg ∠fge and ∠ijl ∠fge and ∠hgj ∠fge and ∠hge

Explanation:

Step1: Recall the definition of vertical angles

Vertical angles are a pair of non - adjacent angles formed by the intersection of two lines. They are opposite each other and are equal in measure.

Step2: Analyze each option

• For $\angle FGE$ and $\angle KJG$: These angles are not formed by the intersection of the same two lines in the required non - adjacent, opposite - each - other way.
• For $\angle FGE$ and $\angle IJL$: These angles are not formed by the intersection of the same two lines in the required non - adjacent, opposite - each - other way.
• For $\angle FGE$ and $\angle HGJ$: When the lines \(EH\) (or \(FG\)) and \(LK\) (or \(JL\)) intersect at point \(G\), \(\angle FGE\) and \(\angle HGJ\) are non - adjacent angles formed by the intersection of these two lines and are opposite each other.
• For $\angle FGE$ and $\angle HGE$: These angles are adjacent (they share a common side \(GE\)) and do not meet the definition of vertical angles.

Answer:

\(\angle FGE\) and \(\angle HGJ\)