Question

df and gi are parallel lines. which angles are alternate interior angles? ∠deh and ∠ihj ∠ghe and ∠feh ∠dec and ∠fec ∠ghe and ∠dec

Explanation:

Step1: Recall the definition of alternate - interior angles

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

Step2: Analyze each option

• For \(\angle DEH\) and \(\angle IHJ\): \(\angle DEH\) is an interior angle with respect to the parallel lines \(DF\) and \(GI\) and transversal \(CJ\), but \(\angle IHJ\) is an exterior angle. So, this pair is not alternate - interior angles.
• For \(\angle GHE\) and \(\angle FEH\): Since \(DF\parallel GI\) and \(CJ\) is the transversal. \(\angle GHE\) and \(\angle FEH\) are non - adjacent, lie between \(DF\) and \(GI\) and on opposite sides of the transversal \(CJ\).
• For \(\angle DEC\) and \(\angle FEC\): These two angles are adjacent (they share a common side \(EC\)) and form a linear pair. So, they are not alternate - interior angles.
• For \(\angle GHE\) and \(\angle DEC\): \(\angle GHE\) is between \(DF\) and \(GI\), but \(\angle DEC\) is not in the correct position (it is not on the opposite side of the transversal in the interior region between the two parallel lines)

Answer:

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