Geometry worksheet titled 'Acrobatic Angles' where students classify angles based on gymnast poses.

Let's solve this step-by-step based on the "Acrobatic Angles" worksheet. The goal is to classify each angle as acute, right, or obtuse by analyzing the stick-figure gymnasts' body positions.

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🔷 Definitions (from the worksheet):

- Acute angle: Less than 90°
- Right angle: Exactly 90°
- Obtuse angle: More than 90° but less than 180°

We’ll go through each numbered angle and analyze it based on the figure.

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## ✔ Figure 1: First gymnast (leftmost)

This gymnast has:
- Vertical body from A to B
- Horizontal arm CD at D
- Arm DE going upward-right
- Leg FG going downward-right

1. ∠ADE

- Point D is where the horizontal arm meets the vertical body.
- From D, arm DE goes up and right.
- So, ∠ADE is the angle between the vertical line AD and the diagonal arm DE.
- This looks less than 90° → Acute

> ✔ Acute

2. ∠ADC

- At point D: between AD (up), DC (left) — horizontal line.
- So this is a straight line, but since DC is horizontal left and AD is vertical up, this forms a 90° angle.
- It’s a corner of an L-shape → Right angle

> ✔ Right

3. ∠BFG

- At point F: between leg FB (down) and leg FG (going down-right).
- The angle opens outward, and it appears greater than 90°, but less than 180° → Obtuse

> ✔ Obtuse

4. ∠EDB

- At point D: between ED (up-right) and DB (down).
- This is the angle from the upper arm to the lower body.
- Since ED is going up and DB is straight down, the angle between them is more than 90° (it's a wide angle).
- Looks like over 90°, so Obtuse

> ✔ Obtuse

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## ✔ Figure 2: Second gymnast (middle-left)

This one has:
- Arms going up-left (D) and up-right (E)
- Body from A to B
- Legs: BC down, CG horizontal right, CF diagonal down-left

5. ∠ABE

- At point B: between AB (up) and BE (up-right)
- The arm BE is angled slightly from the vertical body AB.
- This angle is small, less than 90° → Acute

> ✔ Acute

6. ∠FCG

- At point C: between FC (diagonal down-left) and CG (horizontal right)
- This angle opens widely — more than 90°, less than 180° → Obtuse

> ✔ Obtuse

7. ∠ACG

- At point C: between AC (down) and CG (right)
- This looks like a perfect L-shape → Right angle

> ✔ Right

8. ∠DBE

- At point B: between DB (up-left) and BE (up-right)
- These two arms form a V shape, and the angle between them is greater than 90°, likely around 120–130° → Obtuse

> ✔ Obtuse

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## ✔ Figure 3: Third gymnast (middle-right)

Body: A-B-C-E-F-G
Arms: BC left, BD right
Legs: EF down-left, EG down-right

9. ∠ABC

- At point B: between AB (up) and BC (left)
- This is a corner, forming a 90° angle → Right

> ✔ Right

10. ∠FEG

- At point E: between FE (up-left) and EG (down-right)
- These are legs forming a V shape, opening downward.
- The angle at E is less than 90° → Acute

> ✔ Acute

11. ∠AEG

- At point E: between AE (up) and EG (down-right)
- This spans from top of body to leg.
- The angle is wide, greater than 90° → Obtuse

> ✔ Obtuse

12. ∠CBD

- At point B: between CB (left) and BD (right)
- These are both arms extending left and right from the body.
- The angle is exactly 180°? Wait — no, they're not in a straight line.
- Actually, arms go out at an angle — the angle between them is greater than 90°, but less than 180° → Obtuse

> ✔ Obtuse

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## ✔ Figure 4: Fourth gymnast (rightmost)

Body: A-B-C
Arm: DE going diagonally across the body
Legs: CF horizontal, CG horizontal (but labeled G)

Wait — actually, leg is from C to G (horizontal), and arm from D to E crosses the body.

But let’s examine:

- Point C is the hip.
- Line from C to F is left, C to G is right → so CF and CG are horizontal
- But there’s a small square at point C between CF and CG → that means ∠FCG = 90°, so right angle

Now:

13. ∠DBC

- At point B: between D (arm), B (body), C (down)
- Arm DB is going from B to D (upper left), body BC is down.
- The angle at B between arm and body is less than 90° → Acute

> ✔ Acute

14. ∠EBC

- At point B: between E (arm), B, C (body)
- Arm EB goes to upper right, body BC goes down.
- This angle is wider, more than 90° → Obtuse

> ✔ Obtuse

15. ∠ACF

- At point C: between A (up), C (center), F (left)
- This is the angle from body (up) to leg (left).
- Looks like a 90° angle — and the diagram shows a square symbol at C between AC and CF → Right angle

> ✔ Right

16. ∠ABE

- At point B: between A (up), B, E (arm to upper right)
- This is the same as earlier — arm going up-right from head.
- Angle is less than 90° → Acute

> ✔ Acute

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## ✔ Final Answers:

| # | Angle | Type |
|---|-----------|------------|
| 1 | ∠ADE | Acute |
| 2 | ∠ADC | Right |
| 3 | ∠BFG | Obtuse |
| 4 | ∠EDB | Obtuse |
| 5 | ∠ABE | Acute |
| 6 | ∠FCG | Obtuse |
| 7 | ∠ACG | Right |
| 8 | ∠DBE | Obtuse |
| 9 | ∠ABC | Right |
|10 | ∠FEG | Acute |
|11 | ∠AEG | Obtuse |
|12 | ∠CBD | Obtuse |
|13 | ∠DBC | Acute |
|14 | ∠EBC | Obtuse |
|15 | ∠ACF | Right |
|16 | ∠ABE | Acute |

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## 🎯 Bonus Box:
> Sketch a stick figure showing:
> - One acute angle (e.g., bent elbow),
> - One right angle (e.g., knee at 90°),
> - One obtuse angle (e.g., wide open legs).

You can draw a figure with:
- Bent arm (acute),
- Kneeling leg (right),
- Wide split (obtuse).

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✔ All answers completed! Let me know if you'd like this formatted for printing or want a sketch suggestion.