Unlock the Secrets of Polygons: Interior Angle Sum Calculator

Discover the sum of interior angles for any polygon. Enter the number of sides and visualize the magic of geometry unfold!

Calculate Interior Angle Sum

Enter the number of sides of your polygon to calculate the sum of its interior angles.

Polygon Visualization

Formula for Interior Angle Sum

The sum of the interior angles of a polygon is given by the formula:

$$ Sum = (n - 2) \times 180^\circ $$

Where n is the number of sides.

For a polygon with sides, the sum of the interior angles is: °.

Learn About Interior Angles of Polygons

In geometry, a polygon is a closed shape with straight sides. The interior angles are the angles inside the polygon at each vertex. The sum of these angles depends on the number of sides the polygon has. For example, a triangle (3 sides) has an interior angle sum of 180°, and a quadrilateral (4 sides) has 360°. This calculator helps you find this sum for any polygon. The formula (n-2) × 180° is derived by dividing the polygon into triangles. Each triangle contributes 180° to the total sum.

  • Triangle (3 sides): 180°
  • Quadrilateral (4 sides): 360°
  • Pentagon (5 sides): 540°
  • Hexagon (6 sides): 720°

Source: Wikipedia - Interior Angle