1. What is an Angle Calculator for Polygons?

Definition: This calculator determines the sum of interior angles and each interior angle for regular polygons based on the number of sides.

Purpose: It helps students, architects, and designers quickly calculate angles in geometric shapes without manual computation.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( n \) — Number of sides in the polygon (must be ≥ 3)
• The sum is divided by \( n \) to get each angle in regular polygons

Explanation: The formula derives from dividing the polygon into triangles (each contributing 180°) and counting these triangles.

3. Importance of Angle Calculation

Details: Proper angle calculation is essential for geometric constructions, architectural designs, and engineering projects involving polygonal shapes.

4. Using the Calculator

Tips: Simply enter the number of sides (minimum 3) to get both the total sum of interior angles and each angle in regular polygons.

5. Frequently Asked Questions (FAQ)

Q1: Does this work for all polygons?
A: The sum formula works for all simple polygons. The individual angle calculation assumes a regular polygon (all sides and angles equal).

Q2: What's the minimum number of sides?
A: 3 (triangle). Polygons must have at least 3 straight sides.

Q3: How do I calculate exterior angles?
A: For regular polygons, each exterior angle = 360° ÷ n. The sum is always 360° for any simple polygon.

Q4: What about concave polygons?
A: The sum formula still applies, but individual angles vary in concave polygons (some angles > 180°).

Q5: Can I use decimals for sides?
A: No, the number of sides must be a whole number ≥ 3 as polygons can't have fractional sides.