Let's solve each problem step by step. The goal is to
find the angle (in degrees) of the shaded portion of each circle.
We know that:
- A full circle =
360 degrees
- If a circle is divided into equal parts, each part has an angle of:
$$
\frac{360^\circ}{\text{number of equal parts}}
$$
- Then multiply the number of shaded parts by the angle of one part.
---
1) Half circle shaded (pink)
- Divided into 2 equal parts
- Shaded: 1 part
- Angle: $ \frac{360^\circ}{2} \times 1 = 180^\circ $
✔ Answer: 180°
---
2) Circle divided into 6 equal parts, 4 shaded (blue)
- Each part: $ \frac{360^\circ}{6} = 60^\circ $
- Shaded: 4 parts → $ 4 \times 60^\circ = 240^\circ $
✔ Answer: 240°
---
3) Circle divided into 8 equal parts, 2 shaded (pink)
- Each part: $ \frac{360^\circ}{8} = 45^\circ $
- Shaded: 2 parts → $ 2 \times 45^\circ = 90^\circ $
✔ Answer: 90°
---
4) Circle divided into 10 equal parts, 1 shaded (green)
- Each part: $ \frac{360^\circ}{10} = 36^\circ $
- Shaded: 1 part → $ 1 \times 36^\circ = 36^\circ $
✔ Answer: 36°
---
5) Circle divided into 4 equal parts, 1 shaded (purple)
- Each part: $ \frac{360^\circ}{4} = 90^\circ $
- Shaded: 1 part → $ 90^\circ $
✔ Answer: 90°
---
6) Circle divided into 6 equal parts, 2 shaded (yellow)
- Each part: $ \frac{360^\circ}{6} = 60^\circ $
- Shaded: 2 parts → $ 2 \times 60^\circ = 120^\circ $
✔ Answer: 120°
---
7) Circle divided into 8 equal parts, 2 shaded (orange)
- Each part: $ \frac{360^\circ}{8} = 45^\circ $
- Shaded: 2 parts → $ 2 \times 45^\circ = 90^\circ $
✔ Answer: 90°
---
8) Circle divided into 5 equal parts, 1 shaded (light blue)
- Each part: $ \frac{360^\circ}{5} = 72^\circ $
- Shaded: 1 part → $ 72^\circ $
✔ Answer: 72°
---
9) Circle divided into 6 equal parts, 1 shaded (blue)
- Each part: $ \frac{360^\circ}{6} = 60^\circ $
- Shaded: 1 part → $ 60^\circ $
✔ Answer: 60°
---
10) Circle divided into 3 equal parts, 2 shaded (red)
- Each part: $ \frac{360^\circ}{3} = 120^\circ $
- Shaded: 2 parts → $ 2 \times 120^\circ = 240^\circ $
✔ Answer: 240°
---
11) Circle divided into 8 equal parts, 5 shaded (green)
- Each part: $ \frac{360^\circ}{8} = 45^\circ $
- Shaded: 5 parts → $ 5 \times 45^\circ = 225^\circ $
✔ Answer: 225°
---
12) Circle divided into 6 equal parts, 3 shaded (pink)
- Each part: $ \frac{360^\circ}{6} = 60^\circ $
- Shaded: 3 parts → $ 3 \times 60^\circ = 180^\circ $
✔ Answer: 180°
---
13) Circle divided into 8 equal parts, 6 shaded (light blue)
- Each part: $ \frac{360^\circ}{8} = 45^\circ $
- Shaded: 6 parts → $ 6 \times 45^\circ = 270^\circ $
✔ Answer: 270°
---
14) Circle divided into 10 equal parts, 1 shaded (orange)
- Each part: $ \frac{360^\circ}{10} = 36^\circ $
- Shaded: 1 part → $ 36^\circ $
✔ Answer: 36°
---
15) Circle divided into 8 equal parts, 1 shaded (purple)
- Each part: $ \frac{360^\circ}{8} = 45^\circ $
- Shaded: 1 part → $ 45^\circ $
✔ Answer: 45°
---
✔ Final Answers:
| # | Answer |
|---|--------|
| 1 | 180° |
| 2 | 240° |
| 3 | 90° |
| 4 | 36° |
| 5 | 90° |
| 6 | 120° |
| 7 | 90° |
| 8 | 72° |
| 9 | 60° |
|10 | 240° |
|11 | 225° |
|12 | 180° |
|13 | 270° |
|14 | 36° |
|15 | 45° |
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Let me know if you'd like this in a printable format or need explanations for any specific ones!
Parent Tip: Review the logic above to help your child master the concept of angles of a circle worksheet.
