use the diagrams below to answer #19-23

19. which diagram(s) show adjacent angles? ______

20. which diagram(s) show vertical angles? ______

21. which diagram(s) show complementary angles? ______

22. which diagram(s) show supplementary angles? ______

23. which diagram(s) show a linear pair? ______

Question

use the diagrams below to answer #19-23

19. which diagram(s) show adjacent angles? ______

20. which diagram(s) show vertical angles? ______

21. which diagram(s) show complementary angles? ______

22. which diagram(s) show supplementary angles? ______

23. which diagram(s) show a linear pair? ______

Accepted Answer

### Question 19: Which diagram(s) show adjacent angles?
# Brief Explanations:
Adjacent angles share a common side and vertex.
- Diagram C: Angles 1 and 2 share a common vertex and side.
- Diagram D: Angles 1 and 2 (with the right angle) share a common vertex and side.
- Diagram F: Angles 1 and 2 (with the right angle) share a common vertex and side.
Diagrams A, B, E do not have adjacent angles (A: separate; B: vertical; E: separate).
# Answer: C, D, F

### Question 20: Which diagram(s) show vertical angles?
# Brief Explanations:
Vertical angles are opposite angles formed by intersecting lines. Diagram B has two intersecting lines (one vertical, one slant) forming ∠1 and ∠2 as vertical angles. Other diagrams: A (no intersection), C (adjacent, not vertical), D (includes right angle, not vertical), E (separate), F (includes right angle, not vertical).
# Answer: B

### Question 21: Which diagram(s) show complementary angles?
# Brief Explanations:
Complementary angles sum to $90^\circ$.
- Diagram A: $61^\circ + 29^\circ = 90^\circ$, so complementary.
- Diagram B: If ∠1 and the right angle? Wait, no—wait, vertical angles, but if lines are perpendicular? Wait, no, in B, vertical angles, but if we check, maybe B: ∠1 and the right angle? No, wait, maybe I misread. Wait, Diagram F: ∠1 and ∠2 with right angle: if ∠1 + ∠2 = 90°? Wait, no, let's recheck.
Wait, correct:
- A: $61 + 29 = 90$ (complementary).
- B: If the lines are perpendicular, but vertical angles—wait, no, maybe B: ∠1 and the right angle? No, vertical angles. Wait, maybe D and F: in D, ∠1 and ∠2 with right angle: ∠1 + ∠2 = 90°? Wait, no, the right angle is 90°, so ∠1 + ∠2 = 90°? Wait, maybe the initial answer was wrong. Wait, the user's handwritten answer was A, B, D, F, but let's correct.
Wait, complementary: sum to 90°.
- A: 61 + 29 = 90 ✔️.
- B: If ∠1 and the right angle? No, vertical angles. Wait, maybe B: ∠1 and the angle adjacent? No, vertical angles. Wait, maybe D: ∠1 and ∠2 (with right angle) sum to 90? If the right angle is 90, then ∠1 + ∠2 = 90? Yes, because the vertical line and horizontal line form right angle, so ∠1 + ∠2 = 90. Similarly F: ∠1 + ∠2 = 90. So A (61+29=90), D (∠1+∠2=90), F (∠1+∠2=90), and B? Wait, B: vertical angles, but if the lines are perpendicular, then ∠1 would be 90 - something? No, maybe B is not. Wait, the user's handwritten answer included B, but maybe correct is A, D, F. Wait, no, let's check again.
Wait, the problem is about the diagrams. Let's re-express:
- Diagram A: two angles, 61° and 29°, sum to 90° (complementary) ✔️.
- Diagram B: vertical angles, but if the lines are perpendicular, then ∠1 and the right angle? No, vertical angles. Wait, maybe B: ∠1 and the angle adjacent (the right angle) are complementary? No, vertical angles are equal. Wait, maybe the initial handwritten answer was incorrect. But according to the problem, the correct ones are A (61+29=90), D (∠1 + ∠2 = 90, since right angle), F (∠1 + ∠2 = 90, right angle), and maybe B? No, vertical angles are equal, not necessarily complementary. So maybe A, D, F. But the user's handwritten answer was A, B, D, F. Maybe I made a mistake. Alternatively, maybe B: ∠1 and the right angle? No, vertical angles. Let's proceed with the correct definition: complementary angles sum to 90°. So A (61+29=90), D (∠1 + ∠2 = 90), F (∠1 + ∠2 = 90). So answer: A, D, F. But the user's handwritten answer included B, maybe a mistake. However, based on the diagram, let's confirm:
- A: 61 + 29 = 90 ✔️.
- D: ∠1 and ∠2 with right angle: ∠1 + ∠2 = 90 ✔️.
- F: ∠1 and ∠2 with right angle: ∠1 + ∠2 = 90 ✔️.
So correct answer: A, D, F. But the user's handwritten answer was A, B, D, F. Maybe B is included if ∠1 is 90 - x, but vertical angles are equal. Maybe the diagram B has a right angle, so ∠1 and the right angle? No, adjacent. Wait, maybe the user's answer is correct, but I'm missing. Alternatively, proceed with the correct definition.
# Answer: A, D, F (or as per user's handwritten A, B, D, F—needs diagram clarity, but based on sum 90, A, D, F)

### Question 22: Which diagram(s) show supplementary angles?
# Brief Explanations:
Supplementary angles sum to $180^\circ$.
- Diagram E: $45^\circ + 135^\circ = 180^\circ$, so supplementary.
- Any others? Diagram A: 61+29=90 (complementary), not supplementary. Diagram B: vertical angles, sum not 180. Diagram C: adjacent, sum? Not 180. Diagram D: sum 90. Diagram F: sum 90. So only E? Wait, the user's handwritten answer was A, E. Wait, A: 61+29=90, not 180. So maybe E is correct. Wait, 45 + 135 = 180 ✔️. So answer: E. But user's handwritten was A, E. Maybe mistake. So correct: E.
# Answer: E

### Question 23: Which diagram(s) show a linear pair?
# Brief Explanations:
A linear pair are adjacent angles forming a straight line (sum to $180^\circ$).
- Diagram D: ∠1 and the right angle? No, wait, in D, the vertical line and horizontal line form right angle, so ∠1 and the angle adjacent (forming straight line)? Wait, no. Wait, linear pair: adjacent, sum to 180. Let's check diagrams:
- Diagram D: ∠1 and the angle opposite? No. Diagram F: same as D. Diagram B: vertical angles, not linear pair. Diagram E: separate angles, sum 180 but not adjacent. Diagram C: adjacent, sum? Not 180. Diagram A: separate. Wait, maybe none? But that can't be. Wait, maybe Diagram D: ∠1 and the angle adjacent (forming a straight line with the vertical line). Wait, no, the right angle is 90, so ∠1 + 90 + ∠2 = 180? No, ∠1 + ∠2 = 90. Wait, maybe the correct answer is none, but that's unlikely. Wait, maybe Diagram D: ∠1 and the angle adjacent (the right angle's adjacent) form a linear pair? No. Alternatively, maybe the diagram D has a linear pair. Wait, the problem is unclear, but based on linear pair definition (adjacent, sum 180), maybe Diagram D: ∠1 and the angle adjacent (forming a straight line) sum to 180? No, the right angle is 90. Maybe the answer is D, F? No. Wait, maybe the user's answer is blank, so we need to solve.
Wait, linear pair: adjacent angles that are supplementary (sum 180°). Let's check each diagram:
- A: separate, no.
- B: vertical angles, not adjacent, no.
- C: adjacent, sum? Not 180.
- D: ∠1 and the angle adjacent (the right angle's adjacent) – no, ∠1 + 90 + ∠2 = 180? No, ∠1 + ∠2 = 90.
- E: separate, sum 180, not adjacent.
- F: same as D.
So maybe no diagram shows a linear pair? But that's odd. Alternatively, maybe Diagram D: ∠1 and the angle opposite (vertical angle) – no, vertical angles. Wait, maybe the diagram D has a linear pair. Wait, the right angle is 90, so ∠1 + 90 + ∠2 = 180? No, ∠1 + ∠2 = 90. So maybe the answer is none, but the problem might have a diagram I'm misinterpreting. Alternatively, maybe Diagram D: ∠1 and the angle adjacent (forming a straight line with the vertical line) – no. So the answer is none, but likely I'm missing. Alternatively, maybe Diagram D: ∠1 and the angle adjacent (the right angle) form a linear pair? No, 90 + ∠1 ≠ 180 unless ∠1=90, but it's not. So the answer is $\boxed{\text{None}}$ (or specific diagram if misinterpreted). But based on the given diagrams, maybe D or F, but no. So the answer is none, but the problem might have a different interpretation.

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Explanation:

Question 19: Which diagram(s) show adjacent angles?

Answer:

Question 20: Which diagram(s) show vertical angles?