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I believe this is because you have added an extra angle (consider interior and exterior angle) which is 180 degrees. But, the sum of the exterior angles must always equal 360 degrees. Therefore the whole 180 degrees must be added to the sum of the interior angles. So every side that is added the sum of the interior angles adds up to 180 degrees. Hope that answers your question.

Q: Why does a shape gain 180 degrees every time a side is added to a shape?

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