Question

what is the sum the measures of an octagon.

Answer 1

Your question makes no sense but I will guess you want the interior angles.

The sum of all the exterior angles all the way around anything is 360 degrees.
so with an octagon, each exterior angle is 360/8 = 45 degrees
but the sum of the interior angle and the exterior angle is a straight line, 180
so each interior angle = 180 -45 = 135 degrees