The sum of the interior angles of an octagon is 1080°.
Understanding Polygon Interior Angles
An octagon is defined as a polygon with 8 sides. To find the sum of the interior angles for any polygon, you can use a standard formula based on the number of sides it has.
The formula to calculate the sum of the interior angles of an n-sided polygon is:
(n - 2) × 180°
Applying the Formula to an Octagon
Since an octagon has 8 sides, we substitute n with 8 in the formula:
(8 - 2) × 180°
First, perform the subtraction:
6 × 180°
Then, multiply:
1080°
Therefore, the sum of the interior angles of an octagon is 1080°.
This calculation is consistent whether the octagon is regular (all sides and angles equal) or irregular (sides and angles may differ). The sum of the angles remains the same.
Here's a quick breakdown:
| Polygon Type | Number of Sides (n) | Formula: (n - 2) × 180° | Sum of Interior Angles |
|---|---|---|---|
| Triangle | 3 | (3 - 2) × 180° = 1 × 180° | 180° |
| Quadrilateral | 4 | (4 - 2) × 180° = 2 × 180° | 360° |
| Pentagon | 5 | (5 - 2) × 180° = 3 × 180° | 540° |
| Hexagon | 6 | (6 - 2) × 180° = 4 × 180° | 720° |
| Heptagon | 7 | (7 - 2) × 180° = 5 × 180° | 900° |
| Octagon | 8 | (8 - 2) × 180° = 6 × 180° | 1080° |
The sum of the interior angles of any octagon is indeed 1080°.
