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40 sides
if the exterior angle is 40 degrees the interior angle of the polygon is 180- 40 = 140 degrees. The equation for sides N is interior angle = 180 x (N-2)/N; solving you find N = 9 sides
Exterior angle = 360*9 = 40 degrees. So interior angle = 180 - 40 = 140 deg
180-interior angle = exterior angle 360/exterior angle = number of sides
Interior angle = 140 degrees so exterior angle = 180 - 140 = 40 degrees. Sum of exterior angles = 360 degrees so number of angles = 360/40 = 9 sides.