The sum of the measures of the interior angles of any polygon can be calculated using the formula:
Sum = (n – 2) × 180°
where n is the number of sides in the polygon. For an octagon, which has 8 sides, we can plug in the value:
n = 8
Now, applying this value to our formula:
Sum = (8 – 2) × 180°
Sum = 6 × 180°
Sum = 1080°
Therefore, the sum of the interior angles of an octagon is 1080 degrees. This means that if you were to measure each of the eight interior angles of an octagon and add them together, they would equal 1080 degrees.