Polygon Angle Degrees Calculator

What is a polygon angle?

A polygon is a closed two-dimensional shape with straight sides. The angles of a polygon are the corners where two sides meet. In a regular polygon, all sides and all angles are equal.

There are two main types of polygon angles:

• Interior angles - The angles inside the polygon at each vertex
• Exterior angles - The angles formed by one side and the extension of an adjacent side

For any regular polygon, the sum of all exterior angles is always 360 degrees, regardless of the number of sides.

Interior angle formula

The formula to calculate the interior angle of a regular polygon is:

This formula works because the sum of all interior angles of any polygon is (n - 2) × 180°, and in a regular polygon, this sum is equally divided among all angles.

Exterior angle formula

The formula to calculate the exterior angle of a regular polygon is:

This formula works because the sum of all exterior angles of any polygon is always 360°, and in a regular polygon, this sum is equally divided among all angles.

How to use the calculator

1. Enter the number of sides in the polygon (must be 3 or more)
2. Click the "Calculate" button
3. View the calculated interior and exterior angles
4. Use the chart to visualize the angle relationships

The calculator will display the angles in degrees and show a visual representation of the polygon with its angles.

Examples

Example 1: Triangle (3 sides)

For a triangle (n = 3):

• Interior angle = (3 - 2) × 180° / 3 = 60°
• Exterior angle = 360° / 3 = 120°

Example 2: Square (4 sides)

For a square (n = 4):

• Interior angle = (4 - 2) × 180° / 4 = 90°
• Exterior angle = 360° / 4 = 90°

Example 3: Pentagon (5 sides)

For a pentagon (n = 5):

• Interior angle = (5 - 2) × 180° / 5 = 108°
• Exterior angle = 360° / 5 = 72°