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72 degrees
Providing that it is a regular octagon each exterior angle measures 45 degrees.
Each exterior angle measures 8 degrees
When a polygon is regular, each exterior angle is equal to the other exterior angles. Since the sum of all the exterior angles is 360 degrees, if you divide 360 by the measure of one exterior angle, you will get the number of sides. If you instead have the measure of an interior angle, simply calculate (180 - interior angle measure) to find the measure of the exterior angle, and use the above paragraph.
The measure of 1 exterior angle of a regular 8-sided polygon is equivalent to 45 degrees. Hope I helped! :)