Internal and external angles

In <a href="/facts/Geometry/wTQf5ffQ">geometry</a>, an <a href="/facts/Angle/gFUTEQYq">angle</a> of a <a href="/facts/Polygon/yAq7RjPz">polygon</a> is formed by two adjacent <a href="/facts/Edge_(geometry)/3lFN6sEz">sides</a>. For a <a href="/facts/Simple_polygon/C5CfrPWf">simple polygon</a> (non-self-intersecting), regardless of whether it is <a href="/facts/Polygon/yAq7RjPz">convex or non-convex</a>, this angle is called an internal angle (or interior angle) if a point within the angle is in the interior of the polygon. A polygon has exactly one internal angle per <a href="/facts/Vertex_(geometry)/ID3cea9z">vertex</a>.
If every internal angle of a simple polygon is less than a <a href="/facts/Straight_angle/gFUTEQYq">straight angle</a> (<a href="/facts/Pi/vC0UBj1q">π</a> <a href="/facts/Radian/Srd38Sxa">radians</a> or 180°), then the polygon is called <a href="/facts/Convex_polygon/7x35w610">convex</a>.
In contrast, an external angle (also called a turning angle or exterior angle) is an angle formed by one side of a simple polygon and a <a href="/facts/Extended_side/wtqKRrBS">line extended from an adjacent side</a>.: pp. 261–264

Internal and external angles open-in-new

Internal and external angles