Question

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Explanation:

Step1: Analyze ∠9 & ∠16

∠9 is exterior (left of first vertical line), ∠16 is exterior (right of second vertical line), alternate sides of transversals. So alternate exterior angles (c).

Step2: Analyze ∠15 & ∠11

∠15 and ∠11: ∠15 is below second horizontal, ∠11 above. Alternate interior? Wait, two vertical lines (transversals) and horizontal line (cutting line). Wait, ∠15 and ∠11: ∠15 is interior (between vertical lines), ∠11 is interior, alternate? Wait no, ∠15 is below horizontal, ∠11 above. Wait, maybe none? Wait no, let's recheck. Wait, the two vertical lines are parallel? Assume they are. Then ∠15 and ∠11: ∠15 is at bottom right of second vertical, ∠11 top left of second vertical? No, wait the horizontal line is transversal? Wait, no, the two vertical lines are transversals, and the horizontal line is the cut. Wait, maybe I messed up. Wait, ∠15 is adjacent to ∠11? No. Wait, ∠15 and ∠11: let's see positions. ∠15 is below the horizontal line, between the two vertical lines (interior), ∠11 is above the horizontal line, between the two vertical lines (interior). So alternate interior? Wait, no, alternate interior angles are on opposite sides of transversal. Wait, the transversal here is the horizontal line? No, the vertical lines are transversals. Wait, maybe the problem has two vertical lines (parallel) and a horizontal line (transversal)? Wait, no, the figure has two vertical lines (up-down) and a horizontal line (left-right), intersecting at two points. So the horizontal line is cut by two vertical lines (transversals). So for angles formed by two transversals (vertical lines) and a horizontal line (cut), we need to see. Wait, maybe ∠15 and ∠11: ∠15 is at the bottom intersection, ∠11 at top intersection. ∠15 is below horizontal, ∠11 above. So they are on the same side? No. Wait, maybe none? Wait, no, let's check each:

2. ∠15 & ∠11: Let's list positions. ∠15 is (bottom, between verticals), ∠11 (top, between verticals). So alternate interior angles? Wait, alternate interior angles are on opposite sides of transversal (horizontal line). ∠15 is below horizontal, ∠11 above. So opposite sides. So alternate interior angles (a)? Wait, no, alternate interior are between the two lines (vertical lines) and on opposite sides of transversal (horizontal). So ∠15 (between verticals, below horizontal) and ∠11 (between verticals, above horizontal) – yes, alternate interior (a). Wait, maybe I was wrong earlier.

Step3: Analyze ∠10 & ∠15

∠10 is above horizontal, left of first vertical; ∠15 is below horizontal, right of second vertical. So not alternate, corresponding, vertical, or supplementary. So (f) none? Wait, ∠10 is at top left of first vertical, ∠15 at bottom right of second vertical. No relation. So (f).

Step4: Analyze ∠12 & ∠15

∠12 is top right of second vertical, ∠15 bottom right of second vertical. Vertical angles? No, vertical angles are opposite. ∠12 and ∠16 are vertical, ∠15 and ∠16? No. ∠12 and ∠15: ∠12 is above horizontal, ∠15 below, same vertical line? No, second vertical line. ∠12 is top right, ∠15 bottom right of second vertical. So supplementary? ∠12 + ∠15 = 180? If vertical line is straight, then yes, because they are adjacent and form a linear pair. So supplementary (e).

Step5: Analyze ∠9 & ∠11

∠9 is left of first vertical, above horizontal; ∠11 is right of first vertical, above horizontal (between verticals). So corresponding angles? Wait, ∠9 is at first intersection (top left), ∠11 at second intersection (top left of second vertical). So same position relative to their intersections. So corresponding angles (b).

Step6: Analyze ∠9 & ∠15

∠9 is left of first vertical, above horizontal; ∠15 is right of second vertical, below horizontal. No relation. So (f) none? Wait, ∠9 is exterior (left of first vertical), ∠15 interior (between verticals). No. So (f).

Step7: Analyze ∠13 & ∠14

∠13 and ∠14: they are adjacent, forming a linear pair (supplementary), and also vertical? No, vertical angles are opposite. Wait, ∠13 and ∠14: they are adjacent, forming a straight line (horizontal line? No, vertical line). Wait, the vertical line intersects horizontal line, so ∠13 and ∠14 are adjacent, forming a linear pair (supplementary, e) and also, wait, no: ∠13 and ∠14 are on a vertical line, adjacent, so supplementary (e). Also, are they vertical angles? No, vertical angles are opposite (∠9 and ∠14? No, ∠9 and ∠14: no, ∠9 and ∠13 are vertical? Wait, ∠9 (top left of first vertical), ∠13 (bottom left of first vertical) – those are vertical angles (d). Wait, ∠13 and ∠14: they are adjacent, forming a linear pair, so supplementary (e).

Step8: Analyze ∠9 & ∠15

As before, no relation. (f)

Step9: Analyze ∠14 & ∠11

∠14 is bottom right of first vertical, ∠11 top left of second vertical. ∠14 is interior (between verticals, below horizontal), ∠11 interior (between verticals, above horizontal). So alternate interior angles (a)? Wait, ∠14 is left of second vertical, ∠11 right of first vertical? Wait, ∠14 is at first vertical (left), bottom right; ∠11 at second vertical (right), top left. So between the two verticals (interior), on opposite sides of horizontal transversal. So alternate interior angles (a).

Wait, let's redo each:

1. ∠9 & ∠16: ∠9 (top left, exterior), ∠16 (bottom right, exterior), alternate sides of vertical transversals. So alternate exterior (c).
2. ∠15 & ∠11: ∠15 (bottom, interior), ∠11 (top, interior), alternate sides of horizontal transversal? Wait, no, the transversal is vertical? Wait, maybe the two vertical lines are parallel, and the horizontal line is cut by them. So ∠15 and ∠11: ∠15 is at the bottom intersection, ∠11 at top intersection. ∠15 is below horizontal, ∠11 above. So alternate interior angles (a).
3. ∠10 & ∠15: ∠10 (top right, first vertical), ∠15 (bottom right, second vertical). No relation. (f)
4. ∠12 & ∠15: ∠12 (top right, second vertical), ∠15 (bottom right, second vertical). They are adjacent, forming a linear pair (supplementary, e).
5. ∠9 & ∠11: ∠9 (top left, first vertical), ∠11 (top left, second vertical). Same position relative to their intersections (top, left of verticals). So corresponding angles (b).
6. ∠9 & ∠15: ∠9 (top left, exterior), ∠15 (bottom, interior). No relation. (f)
7. ∠13 & ∠14: ∠13 (bottom left, first vertical), ∠14 (bottom right, first vertical). They are adjacent, forming a linear pair (supplementary, e). Also, are they vertical? No, vertical angles are opposite (∠9 and ∠14? No, ∠9 and ∠13 are vertical (d)? Wait, ∠9 (top left) and ∠13 (bottom left) are vertical angles (d). But ∠13 and ∠14: they are on a vertical line, adjacent, so supplementary (e).
8. ∠14 & ∠11: ∠14 (bottom right, first vertical), ∠11 (top left, second vertical). Between verticals (interior), opposite sides of horizontal transversal. So alternate interior angles (a).

Wait, maybe I made mistakes earlier. Let's confirm each:

1. ∠9 and ∠16: alternate exterior (c) – correct.
2. ∠15 and ∠11: alternate interior (a) – because they are between the two vertical lines (interior) and on opposite sides of the horizontal transversal (∠15 below, ∠11 above).
3. ∠10 and ∠15: no relation (f) – ∠10 is top right of first vertical, ∠15 bottom right of second vertical. Different positions, no angle relation.
4. ∠12 and ∠15: supplementary (e) – they form a linear pair (adjacent, on a straight line, sum to 180°).
5. ∠9 and ∠11: corresponding angles (b) – same position relative to their respective vertical lines (top, left of vertical line).
6. ∠9 and ∠15: none (f) – no angle relation.
7. ∠13 and ∠14: supplementary (e) – adjacent, form a linear pair (sum to 180°). Also, ∠13 and ∠9 are vertical angles (d), but ∠13 and ∠14 are supplementary.
8. ∠14 and ∠11: alternate interior (a) – between vertical lines (interior), opposite sides of horizontal transversal (∠14 below, ∠11 above).

Now, let's answer each:

1. ∠9 & ∠16: (c) alternate exterior angles
2. ∠15 & ∠11: (a) alternate interior angles
3. ∠10 & ∠15: (f) none
4. ∠12 & ∠15: (e) supplementary angles
5. ∠9 & ∠11: (b) corresponding angles
6. ∠9 & ∠15: (f) none
7. ∠13 & ∠14: (e) supplementary angles
8. ∠14 & ∠11: (a) alternate interior angles

But let's check problem 7: ∠13 & ∠14. They are adjacent, forming a straight line (vertical line), so they are supplementary (e) and also, are they vertical angles? No, vertical angles are opposite (∠9 and ∠14? No, ∠9 and ∠13 are vertical (d). Wait, ∠13 and ∠14: they are on a vertical line, adjacent, so supplementary (e) is correct.

Problem 4: ∠12 & ∠15: ∠12 is top right of second vertical, ∠15 bottom right of second vertical. They are adjacent, forming a linear pair (sum to 180°), so supplementary (e).

Problem 5: ∠9 & ∠11: ∠9 is top left of first vertical, ∠11 top left of second vertical. Same position (top, left of vertical line), so corresponding angles (b).

Problem 8: ∠14 & ∠11: ∠14 is bottom right of first vertical (interior, below horizontal), ∠11 top left of second vertical (interior, above horizontal). Between vertical lines (interior), opposite sides of horizontal transversal, so alternate interior (a).

Now, let's present each answer:

1. \boxed{c}
2. \boxed{a}
3. \boxed{f}
4. \boxed{e}
5. \boxed{b}
6. \boxed{f}
7. \boxed{e}
8. \boxed{a}

Wait, but the problem says "answer problems 1-8" – maybe the user wants each answered. So we'll provide each step's answer.

Answer:

1. c
2. a
3. f
4. e
5. b
6. f
7. e
8. a

(Each boxed as per step, but since it's multiple, list each with their answer.)