1. What is a Polygon Interior Angle?

An interior angle of a polygon is the angle formed inside the polygon at one of its vertices. For regular polygons (where all sides and angles are equal), all interior angles are equal.

2. How Does the Calculator Work?

The calculator uses the interior angle formula:

Where:

• \( n \) — Number of sides in the polygon
• Must be an integer ≥ 3

Explanation: The formula comes from the fact that the sum of interior angles of an n-sided polygon is (n-2)×180 degrees, and in a regular polygon, this sum is divided equally among all angles.

3. Importance of Interior Angle Calculation

Details: Calculating interior angles is essential in geometry, architecture, and design. It helps in constructing regular polygons and understanding their properties.

4. Using the Calculator

Tips: Enter the number of sides (must be 3 or more). The calculator will compute the measure of each interior angle in degrees.

5. Frequently Asked Questions (FAQ)

Q1: What's the interior angle of a regular triangle?
A: 60° (n=3: (3-2)×180/3 = 60°)

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

Q3: What happens as the number of sides increases?
A: The interior angle approaches 180° as the polygon becomes more circle-like.

Q4: Can this be used for irregular polygons?
A: No, this formula only gives the angle for regular polygons where all angles are equal.

Q5: What's the relationship between interior and exterior angles?
A: They are supplementary (add up to 180°) in regular polygons.