Sum of Interior Angles of Polygons
Explore how angles change with different polygon shapes
Discover how the sum of interior angles changes with different polygon shapes. Select a polygon type to see its angles and the total sum!
Triangle
Sum of Angles: 180°
Observation:
A triangle has 3 sides and the sum of its interior angles is 180°.
The Mathematics Behind Polygon Angles
Key Formula:
The sum S of the interior angles of an n-sided polygon is given by:
S = (n - 2) × 180°
Where n is the number of sides in the polygon.
Examples:
- Triangle (3 sides): (3-2) × 180° = 180°
- Quadrilateral (4 sides): (4-2) × 180° = 360°
- Pentagon (5 sides): (5-2) × 180° = 540°
- Hexagon (6 sides): (6-2) × 180° = 720°
Why It Works:
Any n-sided polygon can be divided into (n-2) triangles. Since each triangle's angles sum to 180°, multiplying by (n-2) gives the total sum of interior angles for the polygon.
