What is the measure of an exterior angle of a regular octagon?

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The sum of the interior angles of a polygon with n sides is
180(n-2)

A regular octagon has n = 8 (8 equal sides).
The sum of the interior angles is
180*(8 - 2) = 1080°

Because we have a regular octagon, each interior angle is
1080/8 = 135°

The sum of the angles on one side of a straight line is 180°. Therefore the measure of an exterior angle of the regular octagon is 180 - 135 = 45°

  45°