Radian to Degree Conversion Worksheet Worksheet for 5th - 6th ... - Free Printable

Let's solve the Radian to Degree Conversion Worksheet step by step.

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🔷 Formula for Conversion:

To convert from radians to degrees, use the formula:

$$
\text{Degrees} = \text{Radians} \times \left( \frac{180^\circ}{\pi} \right)
$$

We'll apply this formula to each problem.

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✔ Problem-by-Problem Solutions:

#### 1. $ \frac{7\pi}{6} $ rad = ?

$$
\frac{7\pi}{6} \times \frac{180}{\pi} = \frac{7}{6} \times 180 = 210^\circ
$$

✔ Answer: 210°

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#### 2. $ \frac{\pi}{8} $ rad = ?

$$
\frac{\pi}{8} \times \frac{180}{\pi} = \frac{1}{8} \times 180 = 22.5^\circ
$$

✔ Answer: 22.5°

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#### 3. $ \frac{7\pi}{2} $ rad = ?

$$
\frac{7\pi}{2} \times \frac{180}{\pi} = \frac{7}{2} \times 180 = 630^\circ
$$

✔ Answer: 630°

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#### 4. $ \frac{\pi}{3} $ rad = ?

$$
\frac{\pi}{3} \times \frac{180}{\pi} = \frac{1}{3} \times 180 = 60^\circ
$$

✔ Answer: 60°

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#### 5. $ \frac{9\pi}{7} $ rad = ?

$$
\frac{9\pi}{7} \times \frac{180}{\pi} = \frac{9}{7} \times 180 \approx 231.43^\circ
$$

✔ Answer: ≈ 231.43°

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#### 6. $ \frac{5\pi}{2} $ rad = ?

$$
\frac{5\pi}{2} \times \frac{180}{\pi} = \frac{5}{2} \times 180 = 450^\circ
$$

✔ Answer: 450°

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#### 7. $ 8\pi $ rad = ?

$$
8\pi \times \frac{180}{\pi} = 8 \times 180 = 1440^\circ
$$

✔ Answer: 1440°

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#### 8. $ 20 $ rad = ?

$$
20 \times \frac{180}{\pi} \approx \frac{3600}{\pi} \approx 1145.92^\circ
$$

✔ Answer: ≈ 1145.92°

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#### 9. $ 0.77 $ rad = ?

$$
0.77 \times \frac{180}{\pi} \approx 0.77 \times 57.2958 \approx 44.11^\circ
$$

✔ Answer: ≈ 44.11°

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#### 10. $ \frac{3\pi}{5} $ rad = ?

$$
\frac{3\pi}{5} \times \frac{180}{\pi} = \frac{3}{5} \times 180 = 108^\circ
$$

✔ Answer: 108°

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#### 11. $ 1.5 $ rad = ?

$$
1.5 \times \frac{180}{\pi} \approx 1.5 \times 57.2958 \approx 85.94^\circ
$$

✔ Answer: ≈ 85.94°

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#### 12. $ \frac{\pi}{8} $ rad = ?

Wait — this is repeated from #2, but let’s double-check:

$$
\frac{\pi}{8} \times \frac{180}{\pi} = 22.5^\circ
$$

✔ Answer: 22.5°

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#### 13. $ 9 $ rad = ?

$$
9 \times \frac{180}{\pi} \approx \frac{1620}{\pi} \approx 515.66^\circ
$$

✔ Answer: ≈ 515.66°

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#### 14. $ 0.5 $ rad = ?

$$
0.5 \times \frac{180}{\pi} \approx 0.5 \times 57.2958 \approx 28.65^\circ
$$

✔ Answer: ≈ 28.65°

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#### 15. $ \frac{\pi}{10} $ rad = ?

$$
\frac{\pi}{10} \times \frac{180}{\pi} = \frac{1}{10} \times 180 = 18^\circ
$$

✔ Answer: 18°

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#### 16. $ \frac{4\pi}{3} $ rad = ?

$$
\frac{4\pi}{3} \times \frac{180}{\pi} = \frac{4}{3} \times 180 = 240^\circ
$$

✔ Answer: 240°

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📝 Final Answers (All):

| Radians | Degrees |
|--------|---------|
| $ \frac{7\pi}{6} $ | 210° |
| $ \frac{\pi}{8} $ | 22.5° |
| $ \frac{7\pi}{2} $ | 630° |
| $ \frac{\pi}{3} $ | 60° |
| $ \frac{9\pi}{7} $ | ≈ 231.43° |
| $ \frac{5\pi}{2} $ | 450° |
| $ 8\pi $ | 1440° |
| $ 20 $ | ≈ 1145.92° |
| $ 0.77 $ | ≈ 44.11° |
| $ \frac{3\pi}{5} $ | 108° |
| $ 1.5 $ | ≈ 85.94° |
| $ \frac{\pi}{8} $ | 22.5° |
| $ 9 $ | ≈ 515.66° |
| $ 0.5 $ | ≈ 28.65° |
| $ \frac{\pi}{10} $ | 18° |
| $ \frac{4\pi}{3} $ | 240° |

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✔ Summary:

You can now fill in the worksheet with these answers. Remember:
- Use exact values when possible (e.g., $ \frac{7\pi}{6} = 210^\circ $).
- Round decimal approximations to two decimal places unless otherwise specified.

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