Question

ce and fh are parallel lines.
which angles are alternate interior angles?
∠cdg and ∠edg ∠cdg and ∠hgd
∠cdg and ∠edb ∠cdg and ∠cdb

Explanation:

Step1: Recall alternate interior angles definition

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

Step2: Analyze each option

• Option 1: $\angle CDG$ and $\angle EDG$: These are adjacent angles forming a linear pair, not alternate interior.
• Option 2: $\angle CDG$ and $\angle HGD$: $\overleftrightarrow{CE} \parallel \overleftrightarrow{FH}$, transversal is $\overleftrightarrow{IB}$. $\angle CDG$ is between $CE$ and $FH$ (interior), on one side of transversal; $\angle HGD$ is between $CE$ and $FH$ (interior), on opposite side of transversal. So they are alternate interior angles.
• Option 3: $\angle CDG$ and $\angle EDB$: $\angle EDB$ is vertical or corresponding, not alternate interior.
• Option 4: $\angle CDG$ and $\angle CDB$: These are adjacent angles, not alternate interior.

Answer:

$\angle CDG$ and $\angle HGD$ (the option with $\angle CDG$ and $\angle HGD$)