Hexagon Angles- The Complete Degree Count
What Are Hexagon Angles?
A hexagon has 6 vertices and 6 interior angles. That's the starting point. Every hexagon you'll encounter—whether on paper or in the real world—follows the same basic angle rules.
The total degrees in any polygon follow a simple formula: (n-2) Ă— 180, where n is the number of sides. For a hexagon, that's (6-2) Ă— 180 = 720 degrees total interior angle measure.
Interior Angles of a Hexagon
In a regular hexagon—where all sides and angles are equal—each interior angle measures exactly 120 degrees.
Here's how you calculate it:
- Take the total interior angle sum: 720 degrees
- Divide by the number of angles: 6
- Result: 720 Ă· 6 = 120 degrees per angle
For an irregular hexagon, the individual angles can vary. The only requirement is that they still add up to 720 degrees total.
Exterior Angles of a Hexagon
Exterior angles are the angles formed when you extend one side of the hexagon outward. Here's the key fact: the sum of exterior angles for ANY polygon always equals 360 degrees.
For a regular hexagon, each exterior angle measures 60 degrees (360 Ă· 6 = 60).
Interior and exterior angles are supplementary—they add up to 180 degrees. So 120 + 60 = 180. This relationship holds true for every single vertex.
Central Angles of a Hexagon
If you draw lines from the center of a regular hexagon to each vertex, you create 6 central angles. Each one spans from one vertex to the next through the center.
Each central angle measures 60 degrees (360 Ă· 6 = 60). These angles are identical to the exterior angles because they occupy the same positions around the circle.
Angle Comparison Table
| Angle Type | Regular Hexagon | Irregular Hexagon |
|---|---|---|
| Each Interior Angle | 120° | Varies |
| Total Interior Angles | 720° | 720° |
| Each Exterior Angle | 60° | 60° (sum = 360°) |
| Each Central Angle | 60° | N/A (not applicable) |
How to Calculate Hexagon Angles: Step by Step
Finding Interior Angles
Step 1: Count the sides. A hexagon has 6 sides.
Step 2: Apply the formula: (n-2) Ă— 180 = (6-2) Ă— 180 = 720 degrees.
Step 3: For regular hexagons, divide by 6 to get 120 degrees per angle.
Finding Exterior Angles
Step 1: Remember the rule: exterior angles always sum to 360 degrees.
Step 2: Divide 360 by the number of angles (6) for regular hexagons.
Step 3: Result: 60 degrees per exterior angle.
Finding Central Angles
Step 1: Draw lines from the center to each vertex.
Step 2: Divide 360 by the number of central angles created (6).
Step 3: Result: 60 degrees per central angle.
Quick Reference: The Numbers You Need
- Total interior angle sum: 720°
- Regular hexagon interior angle: 120°
- Regular hexagon exterior angle: 60°
- Regular hexagon central angle: 60°
- Interior + Exterior at each vertex: 180°
Why These Angles Matter
Hexagons appear everywhere in engineering and design because of their angle properties. A regular hexagon tiles perfectly without gaps. The 120-degree interior angles allow six hexagons to meet at a single point, forming a seamless pattern.
This is why honeycomb structures use hexagonal shapes—the angles distribute stress evenly and maximize space efficiency.
The Bottom Line
A regular hexagon has 120-degree interior angles and 60-degree exterior and central angles. These numbers aren't arbitrary—they're direct consequences of having six sides and the geometric rules that govern polygons.
For irregular hexagons, interior angles vary but always sum to 720 degrees. Exterior angles still sum to 360 degrees. The formulas don't change.