Sisäkulmansa

Sisäkulmansa is a term used in Finnish geometry to refer to the interior angle at a vertex of a polygon. It is the angle formed by the two sides that meet at that vertex, measured inside the polygon. The possessive form sisäkulmansa indicates a specific interior angle of a particular polygon, as in “kolmion sisäkulmansa.”

In planar Euclidean geometry, the interior angles of a simple polygon have characteristic sums. A polygon with n sides has a total sum of (n − 2) × 180 degrees for all its interior angles. For example, a triangle (n = 3) has a total of 180 degrees, a quadrilateral (n = 4) has 360 degrees, and a pentagon (n = 5) has 540 degrees. If the polygon is regular, all interior angles are equal, and each interior angle of a regular n-gon equals (n − 2) × 180 / n degrees.

Concave polygons demonstrate that interior angles can exceed 180 degrees; the interior angle at a concave vertex is measured inside the polygon but may be greater than a straight angle. The interior angle at a vertex is commonly denoted ∠ABC for a vertex B with adjacent vertices A and C, and it can be computed from side directions or coordinate vectors. When evaluating angles from coordinates, the angle between the vectors BA and BC gives the magnitude of the interior angle, and the result is interpreted as the angle lying inside the polygon.

In Finnish mathematical writing, sisäkulmansa is a standard term in descriptions of polygons, angle sums, and regular-polygon properties. See also interior angle, exterior angle, polygon.