To determine the interior angles of a regular polygon (like the hexagon in the image), you can use the following formula:

\[
\text{Interior Angle} = \frac{(n - 2) \times 180^\circ}{n}
\]

Where \( n \) is the number of sides of the polygon.

### For a hexagon:
- A hexagon has \( n = 6 \) sides.
- Substituting into the formula:

\[
\text{Interior Angle} = \frac{(6 - 2) \times 180^\circ}{6} = \frac{4 \times 180^\circ}{6} = \frac{720^\circ}{6} = 120^\circ
\]

So, the interior angle of a regular hexagon is \( 120^\circ \).

### Explanation:
- The formula \( (n - 2) \times 180^\circ \) calculates the sum of all interior angles in an \( n \)-sided polygon.
- Dividing this sum by \( n \) gives the measure of each interior angle in a regular polygon, where all angles are equal.

This is why I knew that the interior angle of the hexagon in the image was \( 120^\circ \).

Would you like more details or have any further questions?

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### Related Questions:
1. How do you calculate the exterior angle of a regular polygon?
2. What is the relationship between the interior and exterior angles of a polygon?
3. How do the number of sides affect the size of the interior angle in polygons?
4. Can you explain why the sum of the interior angles of a polygon depends on the number of sides?
5. How does the interior angle formula change for irregular polygons?

### Tip:
When working with polygons, remembering that the sum of the interior angles increases by \( 180^\circ \) for each additional side can help you quickly estimate angles and solve related problems.

Learn how to calculate the interior angles of a hexagon using the formula for interior angles of polygons. Step-by-step guide with examples and explanations. Suitable for Grades 9-12.

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