Polygon Exterior Angle Calculator

Exterior Angle: -°

Interior Angle: -°

Sum of Exterior Angles: -°

Sum of Interior Angles: -°

Understanding Polygon Exterior Angles

What are Polygon Exterior Angles?

Exterior angles of a polygon are angles formed between any side of the polygon and the extension of its adjacent side. They play a crucial role in geometry and have several important properties.

Exterior Angle = 360°/n

Interior Angle = 180° - Exterior Angle

Sum of Interior Angles = (n-2) × 180°

Sum of Exterior Angles = 360°

where:

  • n is the number of sides in the polygon
  • Each exterior angle is supplementary to its corresponding interior angle
  • The sum of exterior angles is always 360° for any polygon

Properties of Polygon Angles

  • Each exterior angle of a regular polygon is equal
  • The sum of one exterior and one interior angle at any vertex is 180°
  • The measure of each exterior angle decreases as the number of sides increases
  • As the number of sides approaches infinity, the exterior angle approaches 0°
  • The sum of all exterior angles is constant (360°) regardless of the number of sides
  • In regular polygons, all interior angles are equal, and all exterior angles are equal

Applications and Real-world Examples

Architecture

Used in designing buildings, floor plans, and structural elements

Navigation

Important in calculating turning angles and path planning

Computer Graphics

Essential in polygon modeling and game development

Engineering

Used in mechanical design and robotics

Special Cases and Considerations

  • Triangle (3 sides): Each exterior angle is 120°
  • Square (4 sides): Each exterior angle is 90°
  • Regular Pentagon (5 sides): Each exterior angle is 72°
  • Regular Hexagon (6 sides): Each exterior angle is 60°
  • Regular Octagon (8 sides): Each exterior angle is 45°