Question

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

Explanation:

Step1: Recall the definition of alternate interior angles

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 \(\angle IHE\) and \(\angle DEH\): \(\overrightarrow{DF}\parallel\overrightarrow{GI}\), and \(CJ\) is the transversal. \(\angle IHE\) and \(\angle DEH\) lie between \(\overrightarrow{DF}\) and \(\overrightarrow{GI}\) and on opposite sides of transversal \(CJ\).
• For \(\angle IHE\) and \(\angle IHJ\): These are adjacent angles (they share a common side \(HJ\)), not alternate - interior angles.
• For \(\angle IHE\) and \(\angle DEC\): \(\angle DEC\) is not between the two parallel lines \(\overrightarrow{DF}\) and \(\overrightarrow{GI}\) in the correct position for alternate - interior with \(\angle IHE\).
• For \(\angle IHE\) and \(\angle FEH\): \(\angle FEH\) and \(\angle IHE\) are not in the alternate - interior position (sum of \(\angle FEH\) and \(\angle IHE\) is \(180^{\circ}\) if we consider the parallel lines and transversal, they are same - side interior angles).

Answer:

\(\angle IHE\) and \(\angle DEH\)