Math worksheet for calculating interior and exterior angles of polygons.

You're given a worksheet asking you to find one interior angle, one exterior angle, and the interior angle sum for each polygon shown.

All polygons on this sheet are regular polygons (equal sides and angles), which makes calculations straightforward using standard formulas.

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## ✔ Key Formulas:

For any regular polygon with `n` sides:

1. Sum of Interior Angles = `(n - 2) × 180°`
2. One Interior Angle = `(n - 2) × 180° / n`
3. One Exterior Angle = `360° / n`
*(Also, since interior + exterior = 180°, you can check: exterior = 180° - interior)*

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Let’s identify each polygon by counting its sides (`n`) and then compute the three values.

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🔢 Step-by-Step Solutions:

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#### 1) Regular Octagon → `n = 8`

- Interior Angle Sum = `(8 - 2) × 180 = 6 × 180 = 1080°`
- One Interior Angle = `1080 ÷ 8 = 135.0°`
- One Exterior Angle = `360 ÷ 8 = 45.0°`

✔ Answer 1:
Interior Angle: 135.0°
Exterior Angle: 45.0°
Interior Angle Sum: 1080°

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#### 2) Regular Nonagon → `n = 9`

- Sum = `(9 - 2) × 180 = 7 × 180 = 1260°`
- Interior = `1260 ÷ 9 = 140.0°`
- Exterior = `360 ÷ 9 = 40.0°`

✔ Answer 2:
Interior Angle: 140.0°
Exterior Angle: 40.0°
Interior Angle Sum: 1260°

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#### 3) Regular Octagon → `n = 8` (same as #1)

✔ Answer 3:
Interior Angle: 135.0°
Exterior Angle: 45.0°
Interior Angle Sum: 1080°

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#### 4) Regular Hexagon → `n = 6`

- Sum = `(6 - 2) × 180 = 4 × 180 = 720°`
- Interior = `720 ÷ 6 = 120.0°`
- Exterior = `360 ÷ 6 = 60.0°`

✔ Answer 4:
Interior Angle: 120.0°
Exterior Angle: 60.0°
Interior Angle Sum: 720°

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#### 5) Regular Decagon → `n = 10`

- Sum = `(10 - 2) × 180 = 8 × 180 = 1440°`
- Interior = `1440 ÷ 10 = 144.0°`
- Exterior = `360 ÷ 10 = 36.0°`

✔ Answer 5:
Interior Angle: 144.0°
Exterior Angle: 36.0°
Interior Angle Sum: 1440°

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#### 6) Regular Pentagon → `n = 5`

- Sum = `(5 - 2) × 180 = 3 × 180 = 540°`
- Interior = `540 ÷ 5 = 108.0°`
- Exterior = `360 ÷ 5 = 72.0°`

✔ Answer 6:
Interior Angle: 108.0°
Exterior Angle: 72.0°
Interior Angle Sum: 540°

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#### 7) Regular Pentagon → `n = 5` (same as #6)

✔ Answer 7:
Interior Angle: 108.0°
Exterior Angle: 72.0°
Interior Angle Sum: 540°

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#### 8) Regular Nonagon → `n = 9` (same as #2)

✔ Answer 8:
Interior Angle: 140.0°
Exterior Angle: 40.0°
Interior Angle Sum: 1260°

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#### 9) Regular Decagon → `n = 10` (same as #5)

✔ Answer 9:
Interior Angle: 144.0°
Exterior Angle: 36.0°
Interior Angle Sum: 1440°

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#### 10) Regular Nonagon → `n = 9` (same as #2, #8)

✔ Answer 10:
Interior Angle: 140.0°
Exterior Angle: 40.0°
Interior Angle Sum: 1260°

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#### 11) Regular Decagon → `n = 10` (same as #5, #9)

✔ Answer 11:
Interior Angle: 144.0°
Exterior Angle: 36.0°
Interior Angle Sum: 1440°

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#### 12) Regular Hexagon → `n = 6` (same as #4)

✔ Answer 12:
Interior Angle: 120.0°
Exterior Angle: 60.0°
Interior Angle Sum: 720°

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## 📝 Final Answers Summary:

| Problem | Polygon | Interior Angle | Exterior Angle | Interior Angle Sum |
|---------|---------------|----------------|----------------|--------------------|
| 1 | Octagon | 135.0° | 45.0° | 1080° |
| 2 | Nonagon | 140.0° | 40.0° | 1260° |
| 3 | Octagon | 135.0° | 45.0° | 1080° |
| 4 | Hexagon | 120.0° | 60.0° | 720° |
| 5 | Decagon | 144.0° | 36.0° | 1440° |
| 6 | Pentagon | 108.0° | 72.0° | 540° |
| 7 | Pentagon | 108.0° | 72.0° | 540° |
| 8 | Nonagon | 140.0° | 40.0° | 1260° |
| 9 | Decagon | 144.0° | 36.0° | 1440° |
| 10 | Nonagon | 140.0° | 40.0° | 1260° |
| 11 | Decagon | 144.0° | 36.0° | 1440° |
| 12 | Hexagon | 120.0° | 60.0° | 720° |

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## 💡 Tips for Students:

- Always count the number of sides first.
- Use the formulas — they work for any regular polygon.
- Check your work: Interior + Exterior should equal 180°.
- All answers are rounded to the nearest tenth — but in these cases, all results are whole numbers.

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✔ You’re all set! Fill in the worksheet using the table above. Let me know if you’d like a printable version or step-by-step worked examples for one problem!