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The image shows a partially filled table with columns related to properties of polygons, such as the number of sides, interior angle sum, measure of one interior angle, exterior angle sum, and measure of one exterior angle for regular polygons.

Here’s what the table columns represent:
1. **Number of Sides (n)**
2. **Interior Angle Sum (in degrees)** - Sum of all interior angles of the polygon.
3. **Measure of One Interior Angle (in degrees)** - Interior angle of a regular polygon.
4. **Exterior Angle Sum (in degrees)** - This should always be 360° for any polygon.
5. **Measure of One Exterior Angle (in degrees)** - Exterior angle of a regular polygon.

Let's analyze and fill in the missing data where possible:

### Known Formulas:
1. **Interior Angle Sum**: \((n - 2) \times 180^\circ\)
2. **One Interior Angle (Regular Polygon)**: \(\frac{(n - 2) \times 180^\circ}{n}\)
3. **Exterior Angle Sum**: Always \(360^\circ\) for any polygon.
4. **One Exterior Angle (Regular Polygon)**: \(\frac{360^\circ}{n}\)

### Filling in the Table:
Given the existing data in the table, we can calculate the missing values:

- For **3 sides (Triangle)**:
  - Interior Angle Sum = \( (3 - 2) \times 180^\circ = 180^\circ \)
  - One Interior Angle = \( \frac{180^\circ}{3} = 60^\circ \)
  - One Exterior Angle = \( \frac{360^\circ}{3} = 120^\circ \)
  
- For **4 sides (Quadrilateral)**:
  - Interior Angle Sum = \( (4 - 2) \times 180^\circ = 360^\circ \)
  - One Interior Angle = \( \frac{360^\circ}{4} = 90^\circ \)
  - One Exterior Angle = \( \frac{360^\circ}{4} = 90^\circ \)
  
- For **5 sides (Pentagon)**:
  - Interior Angle Sum = \( (5 - 2) \times 180^\circ = 540^\circ \)
  - One Interior Angle = \( \frac{540^\circ}{5} = 108^\circ \)
  - One Exterior Angle = \( \frac{360^\circ}{5} = 72^\circ \)

- For **6 sides (Hexagon)**:
  - Interior Angle Sum = \( (6 - 2) \times 180^\circ = 720^\circ \)
  - One Interior Angle = \( \frac{720^\circ}{6} = 120^\circ \)
  - One Exterior Angle = \( \frac{360^\circ}{6} = 60^\circ \)
  
- For **7 sides (Heptagon)**:
  - Interior Angle Sum = \( (7 - 2) \times 180^\circ = 900^\circ \)
  - One Interior Angle = \( \frac{900^\circ}{7} \approx 128.57^\circ \)
  - One Exterior Angle = \( \frac{360^\circ}{7} \approx 51.43^\circ \)
  
- For **8 sides (Octagon)**:
  - Interior Angle Sum = \( (8 - 2) \times 180^\circ = 1080^\circ \)
  - One Interior Angle = \( \frac{1080^\circ}{8} = 135^\circ \)
  - One Exterior Angle = \( \frac{360^\circ}{8} = 45^\circ \)
  
Would you like a further detailed breakdown of each step or any other specific help with this table?

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### Relative Questions:
1. What is the formula to calculate the interior angle sum of any polygon?
2. How does the number of sides affect the measure of each exterior angle in a regular polygon?
3. What is the interior angle of a regular decagon?
4. Can the exterior angle sum of any polygon be different from 360°?
5. How would the interior angle sum change for a polygon with 12 sides?
6. If a polygon has an interior angle of 156°, how many sides does it have?
7. What is the relationship between the interior and exterior angles of a regular polygon?
8. How would you derive the formula for the measure of one interior angle of a regular polygon?

### Tip:
Always remember that the exterior angle sum of any polygon, regardless of the number of sides, will always add up to 360°.

Explore the properties of polygons through detailed examples of interior and exterior angles. Learn how to calculate the interior angle sum, measure of one interior angle, and measure of one exterior angle for regular polygons. Includes step-by-step calculations for triangles, quadrilaterals, pentagons, hexagons, heptagons, and octagons.

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