First, look at the sum of the inner angles of a polygon. For any n polygon (n≥3), the sum of its internal angles can be calculated by the following formula: the sum of internal angles = (n-2) × 180 degrees. This formula can be derived by dividing a polygon into n triangles and then calculating the sum of the internal angles of each triangle. For example, for a triangle, the sum of its internal angles is 180 degrees; For a quadrilateral, the sum of its internal angles is 360 degrees.
Next, look at the outer corner of the polygon. The outer angle of a polygon refers to the angle extending outward from the vertex of the polygon. For any n-polygon, the sum of its external angles can also be calculated by the following formula: the sum of external angles = 360 degrees. The derivation of this formula can be obtained by the complementary nature of the outer angle and the inner angle of a polygon. For example, for a triangle, the sum of its outer angles is 360 degrees; For a quadrilateral, the sum of its external angles is also 360 degrees.
Through the method of onion mathematics, the sum of inner angles of polygons can be related to the sum of outer angles. For any N polygon, the sum of its internal angles and the sum of its external angles satisfy the following relationship: sum of internal angles+external angles = n × 180 degrees. This relationship can be obtained by adding each inner corner of a polygon to the adjacent outer corner.
For example, a triangle, the sum of its internal angles is 180 degrees, and the sum of its external angles is also 180 degrees, so that the sum of internal angles and+external angles = 3 × 180 degrees; For a quadrilateral, the sum of its internal angles is 360 degrees, and the sum of its external angles is also 360 degrees, which satisfies that the sum of internal angles and+external angles = 4 × 180 degrees.
onion math
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