The sum of the angle measures of any polygon can be found using the formula:
Sum of interior angles = (n – 2) × 180°
where n is the number of sides of the polygon. For an octagon, which has 8 sides, we can substitute 8 for n in the formula:
Sum of interior angles = (8 – 2) × 180°
This simplifies to:
Sum of interior angles = 6 × 180°
Calculating this gives:
Sum of interior angles = 1080°
Therefore, the sum of the angle measures of an octagon is 1080 degrees.
To visualize this, imagine an octagon and how you could divide it into triangles, each contributing to the overall angle sum. Since each triangle has interior angles summing to 180°, and since an octagon can be divided into 6 triangles (as you can draw 6 non-overlapping triangles from one vertex), it makes sense that the total angle sum will be 6 times 180°.
In conclusion, any time you’re dealing with polygons, you can quickly find the sum of the interior angles using the formula
, thus making it a handy tool for any geometry-related problem!