Question

∠2 and ∠6 are...
alternate exterior angles
alternate interior angles
corresponding angles
same side interior angles

Explanation:

Step1: Recall Angle Relationship Definitions

- **Alternate Exterior Angles**: Angles that lie outside the two lines and on opposite sides of the transversal.
- **Alternate Interior Angles**: Angles that lie between the two lines and on opposite sides of the transversal.
- **Corresponding Angles**: Angles that occupy the same relative position at each intersection where a straight line crosses two others.
- **Same - Side Interior Angles**: Angles that lie between the two lines and on the same side of the transversal.

Step2: Analyze ∠2 and ∠6

- ∠2 is above the top parallel line (line \( t \)) and to the left of the transversal.
- ∠6 is below the bottom parallel line (line \( m \)) and to the left of the transversal. Wait, no, let's re - examine the diagram (assuming two parallel lines \( t \) and \( m \), and a transversal). Wait, actually, ∠2 and ∠6: ∠2 is an upper - left angle at the top intersection, ∠6 is a lower - left angle at the bottom intersection. Wait, no, let's use the correct position.
- Corresponding angles: ∠2 and ∠6. Wait, no, let's think again. Corresponding angles have the same position relative to the parallel lines and the transversal. ∠2 is at the top intersection, above line \( t \), left of transversal. ∠6 is at the bottom intersection, below line \( m \), left of transversal? No, maybe I made a mistake. Wait, actually, in the standard parallel lines and transversal diagram:
- ∠2 and ∠6: Let's see the positions. If we consider the two parallel lines (let's say horizontal lines \( t \) and \( m \)) and a transversal (a slant line). ∠2 is in the upper - left corner of the top intersection, ∠6 is in the lower - left corner of the bottom intersection. Wait, no, corresponding angles are in the same "corner" relative to the parallel lines and transversal. So ∠2 (top - left of top intersection) and ∠6 (bottom - left of bottom intersection) – no, that's not right. Wait, maybe the lines are \( t \) (the two horizontal lines) and the transversal is the slant line. Wait, actually, ∠2 and ∠6: ∠2 is above the top horizontal line, ∠6 is below the bottom horizontal line? No, maybe the correct way is:
- Corresponding angles: When two parallel lines are cut by a transversal, corresponding angles are equal. ∠2 and ∠6: Let's check their positions. ∠2 is at the top intersection, ∠6 is at the bottom intersection. ∠2 is above the top line, ∠6 is below the bottom line? No, maybe the lines are \( t \) (the two vertical - like? No, the diagram has two horizontal lines (let's say \( t \) and \( m \)) and a transversal. Wait, the labels: 1,2,3,4 at the top intersection (with line \( t \)), 5,6,7,8 at the bottom intersection (with line \( m \)). So ∠2 is top - left of top intersection, ∠6 is bottom - left of bottom intersection. Wait, no, corresponding angles are in the same relative position. So ∠1 and ∠5 (top - right and bottom - right), ∠2 and ∠6 (top - left and bottom - left), ∠3 and ∠7 (bottom - right and bottom - right? No, ∠3 is bottom - right of top intersection, ∠7 is bottom - right of bottom intersection), ∠4 and ∠8 (bottom - left of top intersection, bottom - left of bottom intersection). Wait, so ∠2 (top - left of top intersection) and ∠6 (bottom - left of bottom intersection) are corresponding angles because they are in the same "left - top" and "left - bottom" relative to the parallel lines and transversal? Wait, no, maybe I messed up. Wait, alternate exterior angles: ∠2 and ∠7? No. Wait, let's recall the definitions again.
- Alternate Exterior Angles: Angles outside the two parallel lines, on opposite sides of the transversal. ∠2 is outside? No, ∠2 is between the transversal and the top line? Wait, no, the two parallel lines are the two horizontal lines (let's say \( t \) is the top horizontal, \( m \) is the bottom horizontal), and the transversal is the slant line. So the angles above the top horizontal line: ∠1, ∠2; below the bottom horizontal line: ∠7, ∠8; between the two horizontal lines: ∠3, ∠4, ∠5, ∠6. Wait, that can't be. Wait, maybe the two horizontal lines are \( t \) (the upper one) and \( m \) (the lower one), and the transversal is the slant line. So at the top intersection (of transversal and \( t \)): angles 1 (top - right), 2 (top - left), 3 (bottom - right), 4 (bottom - left). At the bottom intersection (of transversal and \( m \)): angles 5 (top - right), 6 (top - left), 7 (bottom - right), 8 (bottom - left). Ah! Now I see. So ∠2 is top - left of top intersection, ∠6 is top - left of bottom intersection. So they are in the same relative position (top - left) at each intersection. So they are corresponding angles.

Answer:

Corresponding Angles