The sum of the interior angles of an octagon can be calculated using a simple formula in geometry. An octagon has eight sides (hence the prefix ‘oct-‘ which means eight). The formula for finding the sum of the interior angles of any polygon is:
Sum of interior angles = (n – 2) × 180°
In this formula, n represents the number of sides in the polygon. For an octagon:
- n = 8
Now, substituting the value of n into the formula:
Sum of interior angles = (8 – 2) × 180°
Sum of interior angles = 6 × 180° = 1080°
Therefore, the sum of the interior angles of an octagon is 1080 degrees.
This means that if you take any octagon and measure all its interior angles, the total will always equal 1080 degrees, regardless of the shape or size of the octagon, as long as it is a simple octagon (not self-intersecting). This concept is crucial in various fields such as architecture, design, and even gaming, where understanding shapes and their properties can play a fundamental role in project success.