1. What is the Angle Sum Formula for Polygons?

Definition: This formula calculates the sum of all interior angles in a polygon based on its number of sides.

Purpose: It helps in geometry problems, architectural design, and any application requiring polygon angle calculations.

2. How Does the Formula Work?

The formula is:

Where:

• \( S \) — Sum of interior angles (degrees)
• \( n \) — Number of sides in the polygon (must be ≥ 3)

Explanation: The formula works because any n-sided polygon can be divided into (n-2) triangles, each with 180°.

3. Importance of Polygon Angle Calculation

Details: Knowing angle sums helps in designing shapes, verifying geometric constructions, and solving complex geometry problems.

4. Using the Calculator

Tips: Simply enter the number of sides (minimum 3) and the calculator will compute the total interior angle sum.

5. Frequently Asked Questions (FAQ)

Q1: What's the angle sum for a triangle?
A: (3-2)×180° = 180°, which matches what we know about triangles.

Q2: What about a quadrilateral?
A: (4-2)×180° = 360°, which is correct for all quadrilaterals.

Q3: Does this work for concave polygons?
A: Yes, the formula works for all simple polygons, whether convex or concave.

Q4: How to find each angle in a regular polygon?
A: Divide the sum by n: \( \frac{(n-2) \times 180°}{n} \).

Q5: Why doesn't the formula work for n < 3?
A: A polygon must have at least 3 sides to enclose an area.