To find the interior angle of a regular polygon, where all sides and angles are equal, 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.

Explanation:

• The sum of the interior angles of any polygon is $(n - 2) \times 180^\circ$.
• Since all angles in a regular polygon are equal, dividing this sum by the number of sides $n$ gives the measure of each interior angle.

Example:

For a regular hexagon (6-sided polygon): $\text{Interior Angle} = \frac{(6 - 2) \times 180^\circ}{6} = \frac{720^\circ}{6} = 120^\circ$

Would you like to try an example with a specific polygon or need more details on this?

5 Related Questions:

1. How do you calculate the exterior angle of a regular polygon?
2. What is the sum of all interior angles of a 12-sided regular polygon?
3. How do the number of sides in a polygon affect the size of its interior angles?
4. What are some real-life applications of regular polygons?
5. How does the formula change for irregular polygons?

Tip: The exterior angle of a regular polygon is complementary to the interior angle and can be calculated as $\frac{360^\circ}{n}$.