It looks like you've uploaded a worksheet titled
"Exterior Angles" that asks students to find the
exterior angle for various regular polygons. The task is to calculate the measure of each exterior angle and round it to the nearest whole number.
Let’s go through this step by step.
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🔷 Key Concept: Exterior Angle of a Regular Polygon
For any
regular polygon (a polygon with all sides and angles equal), the measure of
each exterior angle is:
$$
\text{Exterior Angle} = \frac{360^\circ}{\text{Number of Sides}}
$$
This formula works because the sum of all exterior angles of any polygon is always $360^\circ$, and in a regular polygon, all exterior angles are equal.
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Now, let's solve each problem on the worksheet based on the shapes shown (we'll assume the standard shapes from the description):
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1. Octagon (8 sides)
- Number of sides: 8
- Exterior angle:
$$
\frac{360^\circ}{8} = 45^\circ
$$
✔ Answer:
45°
---
2. Pentagon (5 sides)
- Number of sides: 5
- Exterior angle:
$$
\frac{360^\circ}{5} = 72^\circ
$$
✔ Answer:
72°
---
3. Square (4 sides)
- Number of sides: 4
- Exterior angle:
$$
\frac{360^\circ}{4} = 90^\circ
$$
✔ Answer:
90°
---
4. Heptagon (7 sides)
- Number of sides: 7
- Exterior angle:
$$
\frac{360^\circ}{7} \approx 51.428^\circ \rightarrow \text{Rounded to } 51^\circ
$$
✔ Answer:
51°
---
5. Regular 11-gon (11 sides)
- Number of sides: 11
- Exterior angle:
$$
\frac{360^\circ}{11} \approx 32.727^\circ \rightarrow \text{Rounded to } 33^\circ
$$
✔ Answer:
33°
---
6. Regular 14-gon (14 sides)
- Number of sides: 14
- Exterior angle:
$$
\frac{360^\circ}{14} \approx 25.714^\circ \rightarrow \text{Rounded to } 26^\circ
$$
✔ Answer:
26°
---
7. Regular 13-gon (13 sides)
- Number of sides: 13
- Exterior angle:
$$
\frac{360^\circ}{13} \approx 27.692^\circ \rightarrow \text{Rounded to } 28^\circ
$$
✔ Answer:
28°
---
8. Regular 16-gon (16 sides)
- Number of sides: 16
- Exterior angle:
$$
\frac{360^\circ}{16} = 22.5^\circ \rightarrow \text{Rounded to } 23^\circ
$$
✔ Answer:
23°
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✔ Final Answers Summary:
| Shape | Number of Sides | Exterior Angle |
|------------------|------------------|----------------|
| Octagon | 8 | 45° |
| Pentagon | 5 | 72° |
| Square | 4 | 90° |
| Heptagon | 7 | 51° |
| Regular 11-gon | 11 | 33° |
| Regular 14-gon | 14 | 26° |
| Regular 13-gon | 13 | 28° |
| Regular 16-gon | 16 | 23° |
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📝 Explanation:
- We used the formula:
$$
\text{Exterior Angle} = \frac{360^\circ}{n}
$$
where $ n $ is the number of sides.
- All answers were rounded to the nearest whole number as instructed.
Let me know if you'd like this formatted as a completed worksheet or need help with interior angles too!
Parent Tip: Review the logic above to help your child master the concept of sum of interior angles of a polygon worksheet.
