The measure of an interior angle of a regular octagon can be calculated using the formula for the interior angles of a polygon. For any polygon, the formula is:
Interior Angle = (n – 2) * 180° / n
Where n is the number of sides of the polygon. In the case of a regular octagon, which has 8 sides, we substitute n with 8.
Interior Angle = (8 – 2) * 180° / 8
Calculating this gives:
Interior Angle = 6 * 180° / 8 = 1080° / 8 = 135°
Thus, each interior angle of a regular octagon measures 135 degrees. This means that if you were to draw a regular octagon and measure any of its interior angles, you would find that each one is equal to 135 degrees.