How to Calculate The Degrees of A 6 Sided Polygon

A regular hexagon is a six-sided polygon where all sides and angles are equal. Calculating its interior and exterior degrees is fundamental in geometry, architecture, and design. This guide explains the formulas, provides a calculator, and offers practical examples.

What is a 6-sided polygon?

A six-sided polygon, or hexagon, is a two-dimensional shape with six straight sides. Regular hexagons have all sides and angles equal, while irregular hexagons have varying side lengths and angles. Hexagons appear in nature (honeycombs) and human-made structures (tiles, stop signs).

Did you know? The internal angles of any hexagon always sum to 720 degrees, regardless of its regularity.

Calculating interior degrees

The interior angle of a regular hexagon can be calculated using the formula:

Interior angle = (n - 2) × 180° / n

Where n is the number of sides (6 for a hexagon)

For a hexagon (n = 6):

Interior angle = (6 - 2) × 180° / 6 = 4 × 180° / 6 = 120°

This means each interior angle of a regular hexagon measures 120 degrees. The sum of all interior angles in any hexagon is always 720 degrees (6 × 120°).

Example calculation

If you have a regular hexagon with side length 5 cm, each interior angle is still 120 degrees. The side length affects the perimeter (6 × 5 cm = 30 cm) and area, but not the angle measures.

Calculating exterior degrees

The exterior angle of a regular hexagon is the angle formed outside the shape at each vertex. It can be calculated using:

Exterior angle = 360° / n

Where n is the number of sides (6 for a hexagon)

For a hexagon (n = 6):

Exterior angle = 360° / 6 = 60°

This means each exterior angle of a regular hexagon measures 60 degrees. The sum of all exterior angles in any polygon is always 360 degrees.

Example calculation

If you have a regular hexagon with side length 10 cm, each exterior angle is still 60 degrees. The side length affects the perimeter (6 × 10 cm = 60 cm) and area, but not the angle measures.

Practical applications

Understanding hexagon angles has practical applications in various fields:

Architecture: Hexagonal tiles create interesting patterns in flooring and walls
Engineering: Hexagonal structures provide strength and stability
Art: Hexagonal grids are used in digital art and design
Nature: Honeycomb patterns follow hexagonal geometry

Knowing the angle measures helps in creating precise designs and structures that utilize the inherent properties of hexagons.

Frequently Asked Questions

What is the difference between interior and exterior angles of a hexagon?

Interior angles are the angles inside the hexagon at each vertex, while exterior angles are the angles formed outside the hexagon at each vertex. They are supplementary (add up to 180°) at each vertex.

Can irregular hexagons have different angle measures?

Yes, irregular hexagons can have varying angle measures as long as the sum of all interior angles remains 720 degrees.

How do I measure the angles of a hexagon?

For regular hexagons, use the formulas provided. For irregular hexagons, use a protractor to measure each angle individually, then verify the sum equals 720 degrees.