Octagon Study Guide

Definition

An octagon is a polygon with eight sides and eight angles.

Properties of an Octagon

• Number of Sides: 8
• Number of Angles: 8
• Sum of Interior Angles: (8 - 2) * 180° = 1080°
• Sum of Exterior Angles: 360°
• Each Interior Angle: 135°
• Each Exterior Angle: 45°
• Diagonals: 20 (number of diagonals = 8 * (8 - 3) / 2)

Formulas

Sum of Interior Angles = (n - 2) * 180°

Sum of Exterior Angles = 360°

Each Interior Angle = Sum of Interior Angles / n

Each Exterior Angle = 360° / n

Number of Diagonals = n * (n - 3) / 2

Example

For a regular octagon (where all sides and angles are equal), each interior angle is 135°, and each exterior angle is 45°.