The sum of the internal angles of a polygon: [n-2] × 180 (n is the number of sides); Proof: Take any point O in the N-polygon, connect O with each vertex, and divide the N-polygon into N triangles. Because the sum of the internal angles of these n triangles is equal to n 180, and the sum of the n angles with O as the common vertex is 360.
Introduction to polygons
In mathematics, a plane figure consisting of three or more line segments connected end to end is called a polygon. According to different standards, polygons can be divided into regular polygons and irregular polygons, convex polygons and concave polygons.
Concepts and characteristics of polygons
A closed figure composed of three or more line segments on the same plane but not on the same straight line, which is connected end to end and does not intersect, is called a polygon. A figure composed of many line segments on different planes that are connected end to end and do not intersect is also called a polygon, which is a generalized polygon.
There are at least three line segments that make up a polygon, and a triangle is the simplest polygon. Each line segment that constitutes a polygon is called an edge of the polygon; The common endpoint of two adjacent line segments is called the vertex of the polygon; The angle formed by two adjacent sides of a polygon is called the inner angle of the polygon; The line segment connecting two nonadjacent vertices of a polygon is called the diagonal of the polygon.
The angle formed by the extension line with one side of the inner angle of a polygon opposite to the other side is called the outer angle of the polygon. Take an outer corner of the polygon at each vertex, and their sum is called the sum of the outer corners of the polygon. Polygons can also be divided into regular polygons and non-regular polygons. Regular polygons have equal sides and equal internal angles.
Polygons are divided into planar polygons and spatial polygons. All vertices of a planar polygon are on the same plane, and at least one vertex of a spatial polygon is not on the same plane with other vertices. Polygons can also be divided into convex polygons and concave polygons. All convex polygons are planar polygons (planar polygons are not equal to convex polygons, but also include planar concave polygons), but concave polygons are not all spatial polygons, but there are also planar concave polygons.