The measure of each interior angle of a regular hexagon is 120 degrees.
A regular hexagon is a polygon characterized by six sides of equal length and six interior angles of equal measure. To determine the size of each of these angles, we first need to calculate the total sum of all its interior angles.
Calculating the Sum of Interior Angles of a Hexagon
The general formula for calculating the sum of the interior angles of any polygon is:
(n - 2) × 180°
Where 'n' represents the number of sides of the polygon.
For a hexagon, the number of sides (n) is 6. By substituting this value into the formula, we get:
- Sum of interior angles of a hexagon = (6 - 2) × 180°
- Sum of interior angles of a hexagon = 4 × 180°
- Sum of interior angles of a hexagon = 720°
This means that the total measure of all six interior angles in any hexagon (regular or irregular) is 720 degrees.
Determining Each Interior Angle of a Regular Hexagon
Since a regular hexagon has all its interior angles equal, we can find the measure of a single angle by simply dividing the total sum of the interior angles by the number of angles (which is equal to the number of sides, 6).
- Measure of each interior angle = Sum of interior angles / Number of sides
- Measure of each interior angle = 720° / 6
- Measure of each interior angle = 120°
Therefore, each interior angle in a regular hexagon measures 120 degrees.
Summary of Calculation
| Step | Formula / Calculation | Result |
|---|---|---|
| 1. Number of Sides (n) | For a hexagon | 6 |
| 2. Sum of Interior Angles | (n - 2) × 180° = (6 - 2) × 180° | 720° |
| 3. Measure of Each Interior Angle | Sum of Interior Angles / n = 720° / 6 | 120° |
Properties and Significance of Regular Hexagons
Regular hexagons are not just mathematical curiosities; their unique properties make them prevalent in nature and various engineering applications:
- Optimal Tiling: Regular hexagons are one of the few regular polygons (along with squares and equilateral triangles) that can tile a flat surface perfectly without leaving any gaps or overlaps. This property is famously observed in honeycombs, where the hexagonal cells provide efficient storage and structural stability.
- Symmetry: They exhibit a high degree of symmetry, including 6-fold rotational symmetry and six lines of reflective symmetry, making them visually balanced.
- Structural Efficiency: The hexagonal shape is remarkably efficient in terms of material usage and strength distribution, which is why it's often used in designs for nuts, bolts, and various structural components.
