1. What is the Interior Angle Formula?

The interior angle formula calculates the measure of each interior angle in a regular polygon (a polygon with equal sides and angles). The formula is derived from the sum of interior angles divided by the number of sides.

2. How Does the Calculator Work?

The calculator uses the interior angle formula:

Where:

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

Explanation: The formula works by first calculating the sum of all interior angles (n-2)×180°, then dividing by the number of angles (n).

3. Importance of Polygon Angles

Details: Understanding interior angles is crucial in geometry, architecture, and design. It helps in constructing regular polygons and analyzing 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: A polygon must have at least 3 sides (triangle). 2 sides would just be a line segment.

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

Q3: Does this work for irregular polygons?
A: No, this formula only works for regular polygons where all sides and angles are equal.

Q4: What happens as the number of sides increases?
A: As n approaches infinity, the interior angle approaches 180° (like a circle).

Q5: Can I calculate exterior angles with this?
A: The exterior angle is simply 180° minus the interior angle.