1. Understand the concept of interior angle sum.
The sum of internal angles refers to the sum of all angles inside a polygon. For any polygon, the sum of internal angles is related to the number of sides, and it can also be calculated by some mathematical formulas.
2. Internal Angle and Formula
For a polygon with n sides, the sum of internal angles can be calculated by the following formula: the sum of internal angles =(n-2)× 180 degrees. This formula is based on the characteristics of polygons, where n represents the number of sides of polygons. By substituting n into the formula, we can calculate the sum of the inner angles of the polygon.
for instance
For a triangle, it has three sides, so according to the formula, the sum of its interior angles is: (3-2)× 180 degrees = 180 degrees. For a quadrilateral (rectangle), it has four sides. According to the formula, the sum of internal angles is: (4-2)× 180 degrees =360 degrees. Similarly, for a Pentagon, it has five sides, and the sum of internal angles is: (5-2)× 180 degrees =540 degrees.
4. Derive the formula of internal angle sum
We can understand the internal angle and formula by simple deduction. Taking a quadrilateral as an example, we can divide the quadrilateral into two triangles, and the sum of the internal angles of each triangle is 180 degrees. So the sum of the internal angles of the whole quadrilateral should be the sum of the internal angles of two triangles, which is 360 degrees. Extending to the N-polygon, we can divide it into n-2 triangles, and the sum of the internal angles of each triangle is 180 degrees.
Summary:
The sum of the internal angles of a polygon is determined by the number of sides of the polygon. We can use the formula to calculate the sum of the interior angles of a polygon. The formula is: sum of interior angles =(n-2)× 180 degrees, where n represents the number of sides of the polygon. By understanding the concept and formula of internal angle sum, we can better understand the characteristics and properties of polygons. This is very important for problems involving polygons in geometry and other disciplines.