Interior Angles of a Polygon: The angles inside a polygon formed by two adjacent sides are called interior angles.
Formula for Sum of Interior Angles: For a polygon with \(n\) sides:
\[ \text{Sum of interior angles} = (n - 2) \times 180^\circ \]
Each Interior Angle of a Regular Polygon:
\[ \text{Each interior angle} = \frac{(n - 2) \times 180^\circ}{n} \]
Exterior Angles of a Polygon: An exterior angle is formed by extending one side of a polygon. It is supplementary to the adjacent interior angle.
Important Properties:
- The sum of exterior angles of any polygon (taken one at each vertex) is 360°
- Each exterior angle of a regular polygon = \(\frac{360°}{n}\)
- Interior angle + Exterior angle = \(180°\) (they form a linear pair)
Relationship Table:
| Polygon (n sides) | Sum of Interior Angles | Each Interior Angle (Regular) | Each Exterior Angle (Regular) |
|---|---|---|---|
| Triangle (3) | 180° | 60° | 120° |
| Quadrilateral (4) | 360° | 90° | 90° |
| Pentagon (5) | 540° | 108° | 72° |
| Hexagon (6) | 720° | 120° | 60° |
| Octagon (8) | 1080° | 135° | 45° |