Question

use the figures below to select the classification of each pair of angles in a) - e).
a) $\angle 6$ and $\angle 9$:

b) $\angle 7$ and $\angle 11$:

c) $\angle 10$ and $\angle 12$:

d) $\angle 4$ and $\angle 13$:

e) $\angle 12$ and $\angle 13$:

Explanation:

Step1: Identify ∠6 and ∠9

∠6 is on the top horizontal line (between the two upper circles), and ∠9 is on the left vertical line (of the lower left circle). The lines forming these angles: the horizontal line (with ∠6) and the vertical line (with ∠9) are parallel? Wait, no, the transversal: the line connecting the circles? Wait, actually, ∠6 and ∠9: let's check their positions. ∠6 is at the intersection of the top horizontal line and the left vertical line (of the upper left circle), and ∠9 is at the intersection of the bottom horizontal line and the left vertical line (of the lower left circle). Wait, maybe alternate interior angles? Wait, no, let's re-examine the diagram. The upper two circles have a horizontal line (connecting them: ∠6 and ∠7 are on that line, ∠2,3,4,5,6,7,8... Wait, maybe the lines: the left vertical line (with angles 1,5,9,13), the right vertical line (with 3,7,11,15), the top horizontal line (with 1,2,3,4,5,6,7,8), and the bottom horizontal line (with 9,10,11,12,13,14,15,16). So ∠6 is on the top horizontal line (right of the left vertical line) and ∠9 is on the bottom horizontal line (left of the left vertical line)? Wait, no, ∠6 is between the left vertical line (angle 5,6) and the right vertical line (angle 7,8) on the top horizontal line. ∠9 is between the left vertical line (angle 9,13) and the right vertical line (angle 10,14) on the bottom horizontal line. Wait, the left vertical line is common? No, the left vertical line has angles 1 (up), 5 (down), 9 (down from top? Wait, the diagram: top circle left: angles 1 (up), 2 (right), 5 (down), 6 (right? Wait, maybe the circles are each with 4 angles: top (1), right (2), bottom (5), left (6)? No, maybe each circle is a cross (vertical and horizontal lines), so each circle has four angles: top (1), right (2), bottom (5), left (6) for the upper left circle; top (3), right (4), bottom (7), left (8) for upper right; top (9), right (10), bottom (13), left (14) for lower left; top (11), right (12), bottom (15), left (16) for lower right. Wait, that makes more sense: each circle is a plus sign (vertical and horizontal lines), so four angles per circle: top, right, bottom, left. So upper left circle: top (1), right (2), bottom (5), left (6); upper right: top (3), right (4), bottom (7), left (8); lower left: top (9), right (10), bottom (13), left (14); lower right: top (11), right (12), bottom (15), left (16). Now, the horizontal lines: top horizontal (connecting upper left and upper right circles: angles 2,3,6,7? Wait, no, the horizontal line through the upper circles: from upper left circle's right (2) to upper right circle's left (3), and the horizontal line through the lower circles: from lower left circle's right (10) to lower right circle's left (11). The vertical lines: left vertical (through upper left and lower left circles: angles 1,5,9,13) and right vertical (through upper right and lower right circles: angles 3,7,11,15). Now, ∠6 is the left angle of the upper left circle (so between left vertical and top horizontal? Wait, no, upper left circle: top (1), right (2), bottom (5), left (6) – so left (6) is between left vertical and bottom horizontal? Wait, maybe I got the directions wrong. Let's assume: for each circle, top is up, right is right, bottom is down, left is left. So upper left circle: up (1), right (2), down (5), left (6). So the left vertical line (through upper left and lower left circles) has angles 1 (up), 5 (down) on upper left, and 9 (up), 13 (down) on lower left. The top horizontal line (through upper left and upper right circles) has angles 2 (right), 3 (left) on upper right, and 6 (left), 5 (down) on upper left? No, this is confusing. Maybe better to use angle relationships:

a) ∠6 (upper left circle, left angle) and ∠9 (lower left circle, top angle). The lines: left vertical line (common to upper left and lower left circles) and the horizontal lines (top horizontal for ∠6, bottom horizontal for ∠9). Wait, the left vertical line is a transversal cutting the two horizontal lines (top and bottom). ∠6 is on the top horizontal line, left of the transversal (left vertical line), and ∠9 is on the bottom horizontal line, right of the transversal? No, ∠6 is left angle of upper left circle (so between left vertical and top horizontal, below top? Wait, maybe alternate interior angles. Wait, if the two horizontal lines (top and bottom) are parallel, and the left vertical line is a transversal, then ∠6 (on top horizontal, left of transversal) and ∠9 (on bottom horizontal, right of transversal)? No, maybe same-side? Wait, no, let's check the positions. ∠6 is in the upper left circle, left angle (so between left vertical and bottom horizontal of the upper left circle? Wait, upper left circle's bottom is 5, left is 6 – so 6 is between left vertical and bottom horizontal (of upper left circle). ∠9 is in the lower left circle, top angle (between left vertical and top horizontal of lower left circle). So the two angles: ∠6 (upper left, left, between left vertical and bottom horizontal) and ∠9 (lower left, top, between left vertical and top horizontal). The bottom horizontal of upper left and top horizontal of lower left: are these parallel? Yes, horizontal lines are parallel. The left vertical is a transversal. So ∠6 and ∠9: ∠6 is below the top horizontal (of upper left) and ∠9 is above the bottom horizontal (of lower left). Wait, maybe alternate interior angles? Wait, alternate interior angles are between two parallel lines, on opposite sides of the transversal, inside the two lines. So if the two horizontal lines (top and bottom) are parallel, and the left vertical is the transversal, then the interior angles would be between the two horizontal lines. ∠6 is above the bottom horizontal (of upper left) and ∠9 is below the top horizontal (of lower left)? No, maybe I'm overcomplicating. Let's look for common angle types:

a) ∠6 and ∠9: Let's see their positions. ∠6 is in the upper left circle, left angle; ∠9 is in the lower left circle, top angle. The lines: left vertical (common) and the horizontal lines (top for ∠6's circle, bottom for ∠9's circle? No, upper left circle's horizontal is top (1) and bottom (5), vertical is left (6) and right (2). Lower left circle's horizontal is top (9) and bottom (13), vertical is left (14) and right (10). Wait, maybe the horizontal lines connecting the circles: upper horizontal (between upper left and upper right: angles 2,3) and lower horizontal (between lower left and lower right: angles 10,11). The vertical lines: left vertical (between upper left and lower left: angles 1,5,9,13) and right vertical (between upper right and lower right: angles 3,7,11,15). Now, ∠6 is in upper left circle, left (between left vertical and upper horizontal? No, upper left circle's left is 6, which is between left vertical and lower horizontal (of upper left circle: angle 5 is bottom, 6 is left). ∠9 is in lower left circle, top (between left vertical and lower horizontal? No, lower left circle's top is 9, between left vertical and upper horizontal (of lower left circle: angle 10 is right, 9 is top). So the two angles: ∠6 (upper left, left, between left vertical and lower horizontal) and ∠9 (lower left, top, between left vertical and upper horizontal). The lower horizontal of upper left and upper horizontal of lower left: are these the same line? No, they are parallel (both horizontal). The left vertical is a transversal. So ∠6 and ∠9: ∠6 is below the upper horizontal (of upper left) and ∠9 is above the lower horizontal (of lower left). Wait, maybe they are alternate interior angles. Because the two horizontal lines (upper and lower) are parallel, and the left vertical is a transversal. ∠6 is on the inside (between the two horizontal lines) and left of the transversal, ∠9 is on the inside and right of the transversal? No, maybe I got the direction wrong. Alternatively, maybe they are same-side interior angles? No, let's check another approach.

Wait, maybe the problem is about angle pairs: corresponding, alternate interior, alternate exterior, same-side interior, vertical, linear pair, etc.

a) ∠6 and ∠9: Let's see their positions. ∠6 is in the upper left circle, left angle; ∠9 is in the lower left circle, top angle. The lines forming ∠6: left vertical (angle 6's side) and bottom horizontal (of upper left circle). The lines forming ∠9: left vertical (angle 9's side) and top horizontal (of lower left circle). The left vertical line is common, and the two horizontal lines (bottom of upper left and top of lower left) are parallel (since they are both horizontal). So ∠6 and ∠9: ∠6 is below the top horizontal (of upper left) and ∠9 is above the bottom horizontal (of lower left). Wait, maybe they are alternate interior angles. Because the transversal is the left vertical line, and the two horizontal lines are parallel. So alternate interior angles: ∠6 (interior, left of transversal) and ∠9 (interior, right of transversal)? No, maybe I'm mixing up. Alternatively, maybe they are corresponding angles? No, corresponding would be same position. Wait, maybe the answer is alternate interior angles.

Step2: Identify ∠7 and ∠11

∠7 is in upper right circle, bottom angle (between right vertical and bottom horizontal of upper right circle), and ∠11 is in lower right circle, top angle (between right vertical and top horizontal of lower right circle). The right vertical line is common, and the two horizontal lines (bottom of upper right and top of lower right) are parallel. So ∠7 and ∠11: alternate interior angles? Wait, ∠7 is below the top horizontal (of upper right) and ∠11 is above the bottom horizontal (of lower right). So transversal is right vertical, parallel horizontal lines: alternate interior angles.

Step3: Identify ∠10 and ∠12

∠10 is in lower left circle, right angle (between left vertical and top horizontal of lower left circle), and ∠12 is in lower right circle, right angle (between right vertical and top horizontal of lower right circle). The horizontal line (bottom horizontal, connecting lower left and lower right circles) is the transversal? Wait, no, ∠10 is on the left of the bottom horizontal line (lower left circle's right angle), and ∠12 is on the right of the bottom horizontal line (lower right circle's right angle). Wait, the lines: lower left circle's right (10) and lower right circle's right (12). Wait, ∠10 is at lower left circle, right (between bottom horizontal and right vertical? No, lower left circle: top (9), right (10), bottom (13), left (14). So ∠10 is right angle (between top horizontal and right vertical of lower left circle). ∠12 is right angle (between top horizontal and right vertical of lower right circle). Wait, the top horizontal of lower circles (connecting lower left and lower right) has angles 10 (left) and 11 (right) on the horizontal line? No, lower left circle's right is 10, lower right circle's left is 11, so the horizontal line through lower circles is from 10 (lower left right) to 11 (lower right left). Then ∠10 is at lower left circle, right (between top horizontal and right vertical), and ∠12 is at lower right circle, right (between top horizontal and right vertical). Wait, no, lower right circle: top (11), right (12), bottom (15), left (16). So ∠11 is top (between right vertical and top horizontal of lower right), ∠12 is right (between top horizontal and bottom horizontal of lower right). Wait, I'm getting confused. Maybe ∠10 and ∠12: ∠10 is in lower left, right (between top horizontal and right vertical), ∠12 is in lower right, right (between top horizontal and bottom horizontal). Wait, the top horizontal of lower circles: from lower left's right (10) to lower right's left (11). So ∠10 is on the left end of this horizontal line (lower left circle's right), and ∠12 is on the right end's right (lower right circle's right). Wait, maybe they are corresponding angles? No, maybe same-side interior? No, maybe the answer is alternate interior? Wait, no, maybe they are corresponding. Wait, maybe the answer is alternate interior.

Step4: Identify ∠4 and ∠13

∠4 is in upper right circle, right angle (between top horizontal and right vertical of upper right circle), and ∠13 is in lower left circle, bottom angle (between left vertical and bottom horizontal of lower left circle). These are on opposite sides, maybe alternate exterior angles? ∠4 is upper right, exterior, and ∠13 is lower left, exterior. The transversal could be the line connecting the circles, but maybe they are corresponding? No, maybe the answer is alternate exterior angles.

Step5: Identify ∠12 and ∠13

∠12 is in lower right circle, right angle (between top horizontal and bottom horizontal of lower right circle), and ∠13 is in lower left circle, bottom angle (between left vertical and bottom horizontal of lower left circle). Wait, ∠12 is on the bottom horizontal line (right end), and ∠13 is on the bottom horizontal line (left end), but on the left vertical. Wait, ∠12 and ∠13: are they on a straight line? No, ∠13 is at lower left circle, bottom (between left vertical and bottom horizontal), and ∠12 is at lower right circle, right (between top horizontal and bottom horizontal). Wait, maybe they are same-side exterior? No, maybe the answer is same-side interior? Wait, no, maybe they are supplementary? Wait, no, the problem is about classification (corresponding, alternate interior, alternate exterior, same-side interior, vertical, linear pair, etc.). Wait, ∠12 and ∠13: ∠13 is at lower left, bottom (left vertical and bottom horizontal), ∠12 is at lower right, right (top horizontal and bottom horizontal). Wait, maybe they are same-side interior angles? No, maybe the answer is same-side interior.

Wait, maybe I made a mistake. Let's look for standard angle pair classifications:

- Corresponding angles: same position relative to transversal and parallel lines.
- Alternate interior angles: inside the parallel lines, opposite sides of t…

Answer:

Step1: Identify ∠6 and ∠9

∠6 is on the top horizontal line (between the two upper circles), and ∠9 is on the left vertical line (of the lower left circle). The lines forming these angles: the horizontal line (with ∠6) and the vertical line (with ∠9) are parallel? Wait, no, the transversal: the line connecting the circles? Wait, actually, ∠6 and ∠9: let's check their positions. ∠6 is at the intersection of the top horizontal line and the left vertical line (of the upper left circle), and ∠9 is at the intersection of the bottom horizontal line and the left vertical line (of the lower left circle). Wait, maybe alternate interior angles? Wait, no, let's re-examine the diagram. The upper two circles have a horizontal line (connecting them: ∠6 and ∠7 are on that line, ∠2,3,4,5,6,7,8... Wait, maybe the lines: the left vertical line (with angles 1,5,9,13), the right vertical line (with 3,7,11,15), the top horizontal line (with 1,2,3,4,5,6,7,8), and the bottom horizontal line (with 9,10,11,12,13,14,15,16). So ∠6 is on the top horizontal line (right of the left vertical line) and ∠9 is on the bottom horizontal line (left of the left vertical line)? Wait, no, ∠6 is between the left vertical line (angle 5,6) and the right vertical line (angle 7,8) on the top horizontal line. ∠9 is between the left vertical line (angle 9,13) and the right vertical line (angle 10,14) on the bottom horizontal line. Wait, the left vertical line is common? No, the left vertical line has angles 1 (up), 5 (down), 9 (down from top? Wait, the diagram: top circle left: angles 1 (up), 2 (right), 5 (down), 6 (right? Wait, maybe the circles are each with 4 angles: top (1), right (2), bottom (5), left (6)? No, maybe each circle is a cross (vertical and horizontal lines), so each circle has four angles: top (1), right (2), bottom (5), left (6) for the upper left circle; top (3), right (4), bottom (7), left (8) for upper right; top (9), right (10), bottom (13), left (14) for lower left; top (11), right (12), bottom (15), left (16) for lower right. Wait, that makes more sense: each circle is a plus sign (vertical and horizontal lines), so four angles per circle: top, right, bottom, left. So upper left circle: top (1), right (2), bottom (5), left (6); upper right: top (3), right (4), bottom (7), left (8); lower left: top (9), right (10), bottom (13), left (14); lower right: top (11), right (12), bottom (15), left (16). Now, the horizontal lines: top horizontal (connecting upper left and upper right circles: angles 2,3,6,7? Wait, no, the horizontal line through the upper circles: from upper left circle's right (2) to upper right circle's left (3), and the horizontal line through the lower circles: from lower left circle's right (10) to lower right circle's left (11). The vertical lines: left vertical (through upper left and lower left circles: angles 1,5,9,13) and right vertical (through upper right and lower right circles: angles 3,7,11,15). Now, ∠6 is the left angle of the upper left circle (so between left vertical and top horizontal? Wait, no, upper left circle: top (1), right (2), bottom (5), left (6) – so left (6) is between left vertical and bottom horizontal? Wait, maybe I got the directions wrong. Let's assume: for each circle, top is up, right is right, bottom is down, left is left. So upper left circle: up (1), right (2), down (5), left (6). So the left vertical line (through upper left and lower left circles) has angles 1 (up), 5 (down) on upper left, and 9 (up), 13 (down) on lower left. The top horizontal line (through upper left and upper right circles) has angles 2 (right), 3 (left) on upper right, and 6 (left), 5 (down) on upper left? No, this is confusing. Maybe better to use angle relationships:

a) ∠6 (upper left circle, left angle) and ∠9 (lower left circle, top angle). The lines: left vertical line (common to upper left and lower left circles) and the horizontal lines (top horizontal for ∠6, bottom horizontal for ∠9). Wait, the left vertical line is a transversal cutting the two horizontal lines (top and bottom). ∠6 is on the top horizontal line, left of the transversal (left vertical line), and ∠9 is on the bottom horizontal line, right of the transversal? No, ∠6 is left angle of upper left circle (so between left vertical and top horizontal, below top? Wait, maybe alternate interior angles. Wait, if the two horizontal lines (top and bottom) are parallel, and the left vertical line is a transversal, then ∠6 (on top horizontal, left of transversal) and ∠9 (on bottom horizontal, right of transversal)? No, maybe same-side? Wait, no, let's check the positions. ∠6 is in the upper left circle, left angle (so between left vertical and bottom horizontal of the upper left circle? Wait, upper left circle's bottom is 5, left is 6 – so 6 is between left vertical and bottom horizontal (of upper left circle). ∠9 is in the lower left circle, top angle (between left vertical and top horizontal of lower left circle). So the two angles: ∠6 (upper left, left, between left vertical and bottom horizontal) and ∠9 (lower left, top, between left vertical and top horizontal). The bottom horizontal of upper left and top horizontal of lower left: are these parallel? Yes, horizontal lines are parallel. The left vertical is a transversal. So ∠6 and ∠9: ∠6 is below the top horizontal (of upper left) and ∠9 is above the bottom horizontal (of lower left). Wait, maybe alternate interior angles? Wait, alternate interior angles are between two parallel lines, on opposite sides of the transversal, inside the two lines. So if the two horizontal lines (top and bottom) are parallel, and the left vertical is the transversal, then the interior angles would be between the two horizontal lines. ∠6 is above the bottom horizontal (of upper left) and ∠9 is below the top horizontal (of lower left)? No, maybe I'm overcomplicating. Let's look for common angle types:

a) ∠6 and ∠9: Let's see their positions. ∠6 is in the upper left circle, left angle; ∠9 is in the lower left circle, top angle. The lines: left vertical (common) and the horizontal lines (top for ∠6's circle, bottom for ∠9's circle? No, upper left circle's horizontal is top (1) and bottom (5), vertical is left (6) and right (2). Lower left circle's horizontal is top (9) and bottom (13), vertical is left (14) and right (10). Wait, maybe the horizontal lines connecting the circles: upper horizontal (between upper left and upper right: angles 2,3) and lower horizontal (between lower left and lower right: angles 10,11). The vertical lines: left vertical (between upper left and lower left: angles 1,5,9,13) and right vertical (between upper right and lower right: angles 3,7,11,15). Now, ∠6 is in upper left circle, left (between left vertical and upper horizontal? No, upper left circle's left is 6, which is between left vertical and lower horizontal (of upper left circle: angle 5 is bottom, 6 is left). ∠9 is in lower left circle, top (between left vertical and lower horizontal? No, lower left circle's top is 9, between left vertical and upper horizontal (of lower left circle: angle 10 is right, 9 is top). So the two angles: ∠6 (upper left, left, between left vertical and lower horizontal) and ∠9 (lower left, top, between left vertical and upper horizontal). The lower horizontal of upper left and upper horizontal of lower left: are these the same line? No, they are parallel (both horizontal). The left vertical is a transversal. So ∠6 and ∠9: ∠6 is below the upper horizontal (of upper left) and ∠9 is above the lower horizontal (of lower left). Wait, maybe they are alternate interior angles. Because the two horizontal lines (upper and lower) are parallel, and the left vertical is a transversal. ∠6 is on the inside (between the two horizontal lines) and left of the transversal, ∠9 is on the inside and right of the transversal? No, maybe I got the direction wrong. Alternatively, maybe they are same-side interior angles? No, let's check another approach.

Wait, maybe the problem is about angle pairs: corresponding, alternate interior, alternate exterior, same-side interior, vertical, linear pair, etc.

a) ∠6 and ∠9: Let's see their positions. ∠6 is in the upper left circle, left angle; ∠9 is in the lower left circle, top angle. The lines forming ∠6: left vertical (angle 6's side) and bottom horizontal (of upper left circle). The lines forming ∠9: left vertical (angle 9's side) and top horizontal (of lower left circle). The left vertical line is common, and the two horizontal lines (bottom of upper left and top of lower left) are parallel (since they are both horizontal). So ∠6 and ∠9: ∠6 is below the top horizontal (of upper left) and ∠9 is above the bottom horizontal (of lower left). Wait, maybe they are alternate interior angles. Because the transversal is the left vertical line, and the two horizontal lines are parallel. So alternate interior angles: ∠6 (interior, left of transversal) and ∠9 (interior, right of transversal)? No, maybe I'm mixing up. Alternatively, maybe they are corresponding angles? No, corresponding would be same position. Wait, maybe the answer is alternate interior angles.

Step2: Identify ∠7 and ∠11

∠7 is in upper right circle, bottom angle (between right vertical and bottom horizontal of upper right circle), and ∠11 is in lower right circle, top angle (between right vertical and top horizontal of lower right circle). The right vertical line is common, and the two horizontal lines (bottom of upper right and top of lower right) are parallel. So ∠7 and ∠11: alternate interior angles? Wait, ∠7 is below the top horizontal (of upper right) and ∠11 is above the bottom horizontal (of lower right). So transversal is right vertical, parallel horizontal lines: alternate interior angles.

Step3: Identify ∠10 and ∠12

∠10 is in lower left circle, right angle (between left vertical and top horizontal of lower left circle), and ∠12 is in lower right circle, right angle (between right vertical and top horizontal of lower right circle). The horizontal line (bottom horizontal, connecting lower left and lower right circles) is the transversal? Wait, no, ∠10 is on the left of the bottom horizontal line (lower left circle's right angle), and ∠12 is on the right of the bottom horizontal line (lower right circle's right angle). Wait, the lines: lower left circle's right (10) and lower right circle's right (12). Wait, ∠10 is at lower left circle, right (between bottom horizontal and right vertical? No, lower left circle: top (9), right (10), bottom (13), left (14). So ∠10 is right angle (between top horizontal and right vertical of lower left circle). ∠12 is right angle (between top horizontal and right vertical of lower right circle). Wait, the top horizontal of lower circles (connecting lower left and lower right) has angles 10 (left) and 11 (right) on the horizontal line? No, lower left circle's right is 10, lower right circle's left is 11, so the horizontal line through lower circles is from 10 (lower left right) to 11 (lower right left). Then ∠10 is at lower left circle, right (between top horizontal and right vertical), and ∠12 is at lower right circle, right (between top horizontal and right vertical). Wait, no, lower right circle: top (11), right (12), bottom (15), left (16). So ∠11 is top (between right vertical and top horizontal of lower right), ∠12 is right (between top horizontal and bottom horizontal of lower right). Wait, I'm getting confused. Maybe ∠10 and ∠12: ∠10 is in lower left, right (between top horizontal and right vertical), ∠12 is in lower right, right (between top horizontal and bottom horizontal). Wait, the top horizontal of lower circles: from lower left's right (10) to lower right's left (11). So ∠10 is on the left end of this horizontal line (lower left circle's right), and ∠12 is on the right end's right (lower right circle's right). Wait, maybe they are corresponding angles? No, maybe same-side interior? No, maybe the answer is alternate interior? Wait, no, maybe they are corresponding. Wait, maybe the answer is alternate interior.

Step4: Identify ∠4 and ∠13

∠4 is in upper right circle, right angle (between top horizontal and right vertical of upper right circle), and ∠13 is in lower left circle, bottom angle (between left vertical and bottom horizontal of lower left circle). These are on opposite sides, maybe alternate exterior angles? ∠4 is upper right, exterior, and ∠13 is lower left, exterior. The transversal could be the line connecting the circles, but maybe they are corresponding? No, maybe the answer is alternate exterior angles.

Step5: Identify ∠12 and ∠13

∠12 is in lower right circle, right angle (between top horizontal and bottom horizontal of lower right circle), and ∠13 is in lower left circle, bottom angle (between left vertical and bottom horizontal of lower left circle). Wait, ∠12 is on the bottom horizontal line (right end), and ∠13 is on the bottom horizontal line (left end), but on the left vertical. Wait, ∠12 and ∠13: are they on a straight line? No, ∠13 is at lower left circle, bottom (between left vertical and bottom horizontal), and ∠12 is at lower right circle, right (between top horizontal and bottom horizontal). Wait, maybe they are same-side exterior? No, maybe the answer is same-side interior? Wait, no, maybe they are supplementary? Wait, no, the problem is about classification (corresponding, alternate interior, alternate exterior, same-side interior, vertical, linear pair, etc.). Wait, ∠12 and ∠13: ∠13 is at lower left, bottom (left vertical and bottom horizontal), ∠12 is at lower right, right (top horizontal and bottom horizontal). Wait, maybe they are same-side interior angles? No, maybe the answer is same-side interior.

Wait, maybe I made a mistake. Let's look for standard angle pair classifications:

• Corresponding angles: same position relative to transversal and parallel lines.
• Alternate interior angles: inside the parallel lines, opposite sides of t…