Relationship of Exterior / Interior Angles of a Polygon

The interior angle is always supplementary to an exterior angle at that vertex.
Try this Adjust the polygon below by dragging the orange dot. Notice how the interior angle and exterior angle always add to 180°, even for a concave polygon.

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.

Other polygon topics


Types of polygon

Area of various polygon types

Perimeter of various polygon types

Angles associated with polygons

Named polygons