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The number of sides of a regular polygon is 360 divided by the size of the exterior angle. The external angle is 180 - the internal angle. So for a regular polygon with an internal angle of 135 we get the following. 360 / (180 - 135) = 360 / 45 = 8 sides
That regular polygon would have 9 sides.
Each central angle of a regular 9 sided polygon: 360/9 = 40 degrees
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