Question

select all the pairs of alternate exterior angles.

Explanation:

Step1: Recall alternate - exterior angles definition

Alternate - exterior angles are formed when a transversal intersects two lines. They are outside the two lines and on opposite sides of the transversal.

Step2: Analyze each pair

• For $\angle CDB$ and $\angle HGI$: They are outside the lines $FC$ and $FH$ and on opposite sides of the transversal $IB$, so they are alternate - exterior angles.
• For $\angle EDB$ and $\angle EDG$: $\angle EDB$ and $\angle EDG$ are adjacent angles, not alternate - exterior angles.
• For $\angle EDB$ and $\angle FGI$: They are outside the lines $FC$ and $FH$ and on opposite sides of the transversal $IB$, so they are alternate - exterior angles.
• For $\angle HGD$ and $\angle CDG$: They are outside the lines $FC$ and $FH$ and on opposite sides of the transversal $IB$, so they are alternate - exterior angles.

Answer:

$\angle CDB$ and $\angle HGI$, $\angle EDB$ and $\angle FGI$, $\angle HGD$ and $\angle CDG$