Refer to the figure above. It shows in detail one vertex of the polygon. You can see that the interior angle and exterior angle are supplementary, adding to 180°. As you drag the vertex downwards the polygon becomes concave, with the vertex pushed inwards towards the center of the polygon. As this happens the extended side now moves inside the polygon and the exterior angle becomes negative.
The sum of the interior and exterior angles is still 180° however; you just have to make sure you add them correctly.