The formula for the sum of internal angles is (n-2) × 180 (n is greater than or equal to 3, and n is an integer.

The formula for the sum of internal angles is (n-2) × 180 (n is greater than or equal to 3, and n is an integer.

Knowledge expansion:

The sum of internal angles is a mathematical term, and the sum of all internal angles of a polygon is called the sum of internal angles.

No matter how you change the shape of a polygon, the sum of its internal angles is the same.

Definition of concept

If the number of sides of a polygon remains the same, the sum of the inner angles of the polygon is equal no matter how the shape changes.

Formula of triangle internal angle

After numerous experiments and observations, Thebes Heraclitus, an ancient Greek mathematician and geometer, found an ancient theorem, that is, the formula of the sum of the internal angles of a triangle, that is, the sum of the three internal angles of an arbitrary triangle is equal to 180. This formula, also known as Thebes Theorem, is one of the simplest and most important theorems discovered by geometricians. It has long been a moral criterion for geometricians.

The discovery of this theorem greatly unveiled the veil of geometry, made the ancient Greek geometricians have a deeper understanding of geometry, laid the foundation for a series of new theorems and results, and gave birth to many new discoveries. Before discussing the internal angle and formula of triangle, we need to understand the definition of triangle first. A triangle is a simple polygon, which consists of three line segments, and each side has two internal angles.

The formula of the internal angle of a triangle can be expressed as: a+b+= 180, where A, B and C respectively represent the internal angles of three sides of the triangle. The formula of triangle internal angle sum shows that any triangle has angle sum, and its sum is 180.

According to the formula and the internal angles of the triangle, the sizes of the three internal angles of any triangle can be obtained. According to the nature of a triangle, if the sum of its two internal angles is greater than 180, it is an obtuse triangle; If the sum of its two internal angles is equal to 180, it is a right triangle; If the sum of its two internal angles is less than 180, it is an acute triangle.