Question

which angles are consecutive interior angles?
∠fgd and ∠edb ∠fgd and ∠hgi
∠fgd and ∠fgi ∠fgd and ∠cdg

Explanation:

Step1: Recall consecutive interior angles definition

Consecutive interior angles are two angles that lie between two lines (the "interior") and on the same side of a transversal. The lines \( CE \) and \( FH \) are parallel (implied by the transversal \( BI \)), and \( BI \) is the transversal.

Step2: Analyze each option

- Option 1: \( \angle FGD \) and \( \angle EDB \): \( \angle EDB \) is not between \( CE \) and \( FH \), so not consecutive interior.
- Option 2: \( \angle FGD \) and \( \angle HGI \): \( \angle HGI \) is vertical or adjacent but not between the two lines with the transversal.
- Option 3: \( \angle FGD \) and \( \angle FGI \): These are adjacent angles, not related to the transversal between the two lines.
- Option 4: \( \angle FGD \) and \( \angle CDG \): Wait, correction—wait, let's re - check. Wait, the correct pair: Wait, \( CE \parallel FH \), transversal \( BI \). \( \angle FGD \) and \( \angle CDG \)? Wait, no, wait the first option was \( \angle FGD \) and \( \angle EDB \)? Wait, no, maybe I misread. Wait, the correct consecutive interior angles: \( \angle FGD \) and \( \angle EDB \)? No, wait \( CE \) and \( FH \) are the two lines, transversal \( BI \). So \( \angle FGD \) (between \( FH \) and \( BI \)) and \( \angle EDB \) (between \( CE \) and \( BI \))? Wait, no, \( \angle CDG \) is same as \( \angle EDB \)? Wait, no, let's look at the angles. \( \angle FGD \) is at \( G \) between \( FH \) and \( BI \), and \( \angle CDG \) (or \( \angle EDB \)) is at \( D \) between \( CE \) and \( BI \), on the same side of the transversal. Wait, but the first option is \( \angle FGD \) and \( \angle EDB \). Wait, maybe the correct answer is \( \angle FGD \) and \( \angle EDB \)? Wait, no, let's recall the definition again. Consecutive interior angles are also called same - side interior angles. So for two parallel lines cut by a transversal, same - side interior angles are supplementary. So \( CE \parallel FH \), transversal \( BI \). \( \angle FGD \) is inside \( FH \) and \( BI \), and \( \angle CDG \) (which is equal to \( \angle EDB \)) is inside \( CE \) and \( BI \), on the same side of the transversal. Wait, but among the options, the first option is \( \angle FGD \) and \( \angle EDB \). Wait, maybe I made a mistake. Wait, let's check the options again:

Wait, the options are:

1. \( \angle FGD \) and \( \angle EDB \)

2. \( \angle FGD \) and \( \angle HGI \)

3. \( \angle FGD \) and \( \angle FGI \)

4. \( \angle FGD \) and \( \angle CDG \)

Wait, \( \angle CDG \) and \( \angle EDB \) are vertical angles? No, \( \angle CDG \) and \( \angle EDB \) are actually the same angle? Wait, no, \( CD \) and \( DE \) are a straight line, \( FG \) and \( GH \) are a straight line. Transversal \( BI \). So \( \angle FGD \) (at \( G \), between \( FH \) and \( BI \)) and \( \angle EDB \) (at \( D \), between \( CE \) and \( BI \)) are same - side interior angles (consecutive interior angles) because they are between the two lines (\( CE \) and \( FH \)) and on the same side of the transversal \( BI \).

Wait, but let's check the other options again:

- \( \angle FGD \) and \( \angle HGI \): \( \angle HGI \) is vertical to \( \angle FGB \) or something, not between the two lines.

- \( \angle FGD \) and \( \angle FGI \): These are adjacent angles forming a linear pair, not consecutive interior.

- \( \angle FGD \) and \( \angle CDG \): \( \angle CDG \) is at \( D \), but \( \angle CDG \) and \( \angle FGD \): Wait, \( CD \parallel FG \)? No, \( CE \parallel FH \). So \( \angle FGD \) and \( \angle EDB \) (which is equal to \( \angle CDG \)) are same - side interior. So the correct option is the first one: \( \angle FGD \) and \( \angle EDB \)

Answer:

\( \angle FGD \) and \( \angle EDB \) (assuming the first option is labeled as, for example, A. \( \angle FGD \) and \( \angle EDB \), then the answer is A. \( \angle FGD \) and \( \angle EDB \))