Question

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

Explanation:

Step1: Recall alternate - interior angles definition

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

Step2: Analyze each pair of angles

For the parallel lines $\overleftrightarrow{GI}$ and $\overleftrightarrow{DF}$ with transversal $\overleftrightarrow{JC}$, $\angle IHE$ and $\angle DEH$ are non - adjacent, between the parallel lines $\overleftrightarrow{GI}$ and $\overleftrightarrow{DF}$, and on opposite sides of the transversal $\overleftrightarrow{JC}$.

• $\angle IHE$ and $\angle FEC$ are not alternate - interior angles as they are not on the opposite sides of the transversal in the correct way.
• $\angle IHE$ and $\angle DEC$ are not alternate - interior angles.
• $\angle IHE$ and $\angle IHJ$ are adjacent angles, not alternate - interior angles.

Answer:

$\angle IHE$ and $\angle DEH$