Calculate Decagon Angle

Decagon Interior Angle Formula:

\[ \text{Interior Angle} = \frac{(n - 2) \times 180°}{n} \] \[ \text{For decagon (n=10):} \] \[ \text{Interior Angle} = \frac{(10 - 2) \times 180°}{10} = 144° \]

Interior Angle:

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1. What is a Decagon Angle?

A decagon is a 10-sided polygon. The interior angle of a regular decagon is 144°. This calculator computes interior angles for any regular polygon, with decagon as the default example.

2. How Does the Calculator Work?

The calculator uses the interior angle formula:

\[ \text{Interior Angle} = \frac{(n - 2) \times 180°}{n} \]

Where:

\( n \) — Number of sides (10 for decagon)
180° — Total degrees in a triangle

Explanation: The formula divides the polygon into (n-2) triangles, then calculates the angle for each vertex.

3. Importance of Interior Angles

Details: Knowing interior angles is essential for geometric constructions, architectural design, and tiling patterns. Regular decagons appear in nature and human-made designs.

4. Using the Calculator

Tips: Enter number of sides (≥3). Default is 10 for decagon. The calculator works for any regular polygon.

5. Frequently Asked Questions (FAQ)

Q1: What's the exterior angle of a decagon?
A: 36° (since exterior + interior = 180°)

Q2: Can this calculate angles for irregular polygons?
A: No, this only works for regular (equal-sided) polygons.

Q3: What's the sum of all interior angles?
A: For decagon: (10-2)×180° = 1440°

Q4: How is this used in real life?
A: Applications include tiling patterns, structural engineering, and graphic design.

Q5: What's the angle for other common polygons?
A: Triangle: 60°, Square: 90°, Pentagon: 108°, Hexagon: 120°