Exterior angle theorem sum of angles of a triangle is 180°. If it is known that the sum of the measures of the angles in a triangle is 180°, then the HSEAT is proved as follows: On the other hand, if the HSEAT is taken as a true statement then: Proving that the sum of the measures of the angles of a triangle is 180°. The Euclidean proof of the HSEAT (and simultaneously the result on the sum of the angles of a triangle) starts by constructing the line parallel to side "AB" passing through point "C" and then using the properties of
Internal and external angles simple polygon and a line extended from an adjacent side. The interior angle concept can be extended in a consistent way to crossed polygons such as star polygons by using the concept of directed angles. In general, the interior angle sum in degrees of any closed polygon, including crossed (self-intersecting) ones, is then given by 180("n"–2"k")° where "n" is the number of vertices and the non-negative number "k" is the number of total revolutions of 360° one undergoes walking around the perimeter of the polygon. In other words, 360"k"° represents the sum of all the exterior angles. For example, for