1. What is a Regular Polygon?

A regular polygon is a shape with all sides equal in length and all interior angles equal in measure. Examples include equilateral triangles, squares, regular pentagons, etc.

2. How Does the Calculator Work?

The calculator uses the interior angle formula for regular polygons:

Where:

• \( n \) — Number of sides (must be ≥3)
• 180° — Sum of angles in a triangle

Explanation: The formula works by dividing the polygon into (n-2) triangles, then dividing the total degrees by the number of angles.

3. Importance of Polygon Angles

Details: Knowing interior angles is essential in geometry, architecture, engineering, and design. It helps in constructing precise shapes and understanding their properties.

4. Using the Calculator

Tips: Simply enter the number of sides (must be 3 or more) and click calculate. The result will show the measure of each interior angle in degrees.

5. Frequently Asked Questions (FAQ)

Q1: What's the smallest number of sides a polygon can have?
A: Three sides (triangle). Two sides wouldn't form a closed shape.

Q2: What's the interior angle of a regular pentagon?
A: 108° (calculated as (5-2)×180/5 = 540/5 = 108°)

Q3: How do you calculate exterior angles?
A: Exterior angle = 360° divided by number of sides (n)

Q4: What happens as the number of sides increases?
A: The interior angle approaches 180° as the polygon becomes more circle-like.

Q5: Can this be used for irregular polygons?
A: No, this formula only works for regular polygons where all angles are equal.