Calculating Degrees of 6 Sided Polygon

A regular hexagon is a six-sided polygon where all sides and angles are equal. Calculating the interior and exterior degrees of a hexagon is essential in geometry, architecture, and design. This guide explains how to determine these angles and provides an interactive calculator for quick calculations.

What is a 6-sided polygon?

A six-sided polygon, also known as a hexagon, is a two-dimensional shape with six straight sides. A regular hexagon has all sides of equal length and all interior angles equal. Hexagons are common in nature, such as in honeycombs, and in human-made structures like stop signs and floor tiles.

Understanding the angles of a hexagon is fundamental in geometry. The sum of the interior angles of any polygon can be calculated using the formula:

Sum of interior angles = (n - 2) × 180° where n is the number of sides

For a hexagon (n = 6):

Sum of interior angles = (6 - 2) × 180° = 720°

Calculating interior degrees

The interior angle of a regular hexagon can be calculated by dividing the total sum of interior angles by the number of sides.

Interior angle = Sum of interior angles ÷ Number of sides = 720° ÷ 6 = 120°

Therefore, each interior angle of a regular hexagon measures 120 degrees.

In a regular hexagon, all interior angles are equal. For irregular hexagons, the angles can vary, but the sum of all interior angles will always be 720 degrees.

Calculating exterior degrees

The exterior angle of a polygon is the angle formed by one side and the extension of an adjacent side. For a regular polygon, each exterior angle can be calculated by dividing 360 degrees by the number of sides.

Exterior angle = 360° ÷ Number of sides = 360° ÷ 6 = 60°

Therefore, each exterior angle of a regular hexagon measures 60 degrees.

An important property of polygons is that the sum of an interior and exterior angle at any vertex is always 180 degrees. For a regular hexagon:

Interior angle + Exterior angle = 120° + 60° = 180°

Example calculation

Let's calculate the interior and exterior angles of a regular hexagon:

Determine the sum of interior angles: (6 - 2) × 180° = 720°
Calculate the interior angle: 720° ÷ 6 = 120°
Calculate the exterior angle: 360° ÷ 6 = 60°

This means each interior angle is 120 degrees and each exterior angle is 60 degrees in a regular hexagon.

Hexagon Angle Summary
Angle Type	Calculation	Result
Sum of interior angles	(6 - 2) × 180°	720°
Interior angle	720° ÷ 6	120°
Exterior angle	360° ÷ 6	60°

FAQ

What is the difference between interior and exterior angles?: The interior angle is the angle inside the polygon at a vertex, while the exterior angle is the angle formed by one side and the extension of an adjacent side. They are supplementary (add up to 180°).
Can I calculate the angles of an irregular hexagon?: Yes, you can calculate the sum of interior angles of any hexagon using the formula (n - 2) × 180°, but individual angles will vary unless it's a regular hexagon.
How are hexagon angles used in real life?: Hexagon angles are used in architecture, engineering, and design to create stable structures and patterns. They appear in honeycombs, stop signs, and various tiling patterns.
What if I have a polygon with more than six sides?: The same formulas apply. For an n-sided polygon, the sum of interior angles is (n - 2) × 180°, and each interior angle is (n - 2) × 180° ÷ n.