Question

df and gf are parallel lines. which angles are alternate interior angles? ∠feh and ∠dec ∠feh and ∠ghe ∠feh and ∠deh ∠feh and ∠ghj

Explanation:

Step1: Recall alternate - interior angles definition

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

Step2: Analyze each option

• For \(\angle FEH\) and \(\angle DEC\): These are vertical angles (opposite angles formed by the intersection of two lines \(DF\) and \(CJ\)), not alternate - interior angles.
• For \(\angle FEH\) and \(\angle GHE\): Since \(DF\parallel GI\) and \(CJ\) is the transversal, \(\angle FEH\) and \(\angle GHE\) lie between \(DF\) and \(GI\) and on opposite sides of the transversal \(CJ\).
• For \(\angle FEH\) and \(\angle DEH\): These are adjacent angles (they share a common side \(EH\) and a common vertex \(E\)), not alternate - interior angles.
• For \(\angle FEH\) and \(\angle GHJ\): \(\angle GHJ\) is not in the correct position (not between the two parallel lines \(DF\) and \(GI\) in the sense of alternate - interior angles with respect to the transversal \(CJ\)).

Answer:

\(\angle FEH\) and \(\angle GHE\)