1. What are Interior and Exterior Angles?

Interior angles are the angles inside a polygon formed by two adjacent sides. Exterior angles are formed by extending one side of the polygon and measuring the angle between this extension and the adjacent side. The sum of interior angles in any polygon is (n-2) × 180°.

2. How Does the Calculator Work?

The calculator uses the following formulas:

Where:

• \( n \) — Number of sides in the polygon

Explanation: For any regular polygon, all interior angles are equal, and all exterior angles are equal. The exterior angles always sum to 360°.

3. Importance of Angle Calculation

Details: Calculating interior and exterior angles is essential in geometry, architecture, engineering, and design. It helps in understanding polygon properties, constructing regular shapes, and solving geometric problems.

4. Using the Calculator

Tips: Enter the number of sides (must be 3 or greater) of the regular polygon. The calculator will compute both interior and exterior angles in degrees.

5. Frequently Asked Questions (FAQ)

Q1: What is the minimum number of sides required?
A: The minimum number of sides is 3, which represents a triangle. Polygons must have at least 3 sides.

Q2: Do these formulas work for irregular polygons?
A: No, these formulas are specifically for regular polygons where all sides and angles are equal. Irregular polygons have varying interior angles.

Q3: What is the relationship between interior and exterior angles?
A: For any polygon, interior angle + exterior angle = 180° at each vertex. They are supplementary angles.

Q4: Can these formulas be used for circles?
A: No, circles are not polygons. A circle has 360 degrees but no sides in the polygonal sense.

Q5: What happens as the number of sides increases?
A: As n increases, the interior angle approaches 180° and the exterior angle approaches 0°. A polygon with many sides approximates a circle.