What does the inner angle of a polygon have to do with the number of its sides

The sum of the internal angles of the n-sided shape is equal to (n-2) 180°

The reasons are as follows: triangle and quadrilateral interior angles and pentagonal interior angles and hexagonal interior angles.

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From the above reasoning, it can be calculated that (n-3) diagonals can be drawn through a certain vertex of the n-sided shape, and the n-sided shape can be divided into (n-2) triangles, and the sum of the internal angles of the (n-2) triangle is equal to the sum of the internal angles of the n-side, that is, the sum of the internal angles of the polygon is: (n-2) 180°

Answer: The relationship between the inner angles of a polygon and the number of its sides is: the sum of the internal angles of the polygon = (n-2) 180°

2) When n=8, (n-2) 180°=6 180°=1080°, A: The sum of the inner angles of the octagon is 1080°

So the answer is: 540°; 720°；(1) Sum of polygon inner angles = (n-2) 180°; （2）1080；（n-2）•180°．

Triangles connect diagonals The triangle is divided into 1.

The quadrilateral is divided into 2.

The pentagonal shape is divided into 3 pieces.

The n-sided shape is divided into n-2.

Because the inner angles of each triangle are 180 degrees, the relationship between the inner angles of a polygon and the number of its sides is.

n-2) *180 degrees.

Hope Roy

It should be the number of sides -2 times 180 degrees.

The sum of the inner angles of a polygon with the variable n is (n-2)*180

The sum of the internal angles of a polygon and the number of its edges is the sum of the inner angles of a polygon = (number of sides -2) 180°. A polygon is composed of three or more line segments connected sequentially from end to end, and the empty chain is called a polygon. According to different standards, polygons can be divided into regular and non-regular polygons, convex polygons and concave polygons.

There are at least 3 line segments that make up a polygon, with triangles being the simplest polygons. Each line segment that makes up a polygon is called an edge of the polygon; The common endpoints of the two adjacent line segments are called the vertices of the polygon; The angles formed by the adjacent sides of a polygon are called the inner angles of the polygon; The line segment that connects two non-adjacent vertices of a polygon is called the diagonal of the polygon.

The sum of the internal angles of the polygon = (number of sides - 2) 180 degrees (n is greater than or equal to 3 and n is an integer). According to the inner angle of the triangle and the derivation, it is calculated that from one vertex to connect the other vertices separately into n-2 triangles, n represents the number of sides.

An isosceles triangle is formed by the lines of any two adjacent sides of a polygon.

Evidence 1:Take any point o in the n-side, connect the o to the vertices, and divide the n-side into n triangles.

Because the sum of the inner angles of the n triangles is equal to n·180°, the sum of the n angles with o as the common vertex is 360°

So the sum of the inner angles of the n-sided is n·180°-2 180°=(n-2)·180°

That is, the sum of the internal angles of the n-sided is equal to (n-2) 180° (n is the number of sides).

Evidence 2:Connecting the segments of any vertex A1 of the polygon to its vertices that are not adjacent to it, dividing the n-sided into (n-2) triangles.

Because the sum of the inner angles of the (n-2) triangle is equal to (n-2)·180° (n is the number of sides).

So the sum of the inner angles of the n-sided is (n-2) 180°

Evidence 3:Take any point p on either side of the n-edge, and connect the line segments that connect the p point to other vertices that are not adjacent to the n-side to divide the n-side into (n-1) triangles.

The sum of the internal angles of the (n-1) triangle is equal to (n-1)·180° (n is the number of sides).

The sum of the (n-1) angles with p as the common vertex is 180°

So the sum of the internal angles of the n-sided is (n-1)·180°-180°=(n-2)·180° (n is the number of sides).

Triangles connect diagonals The triangle is divided into 1.

The quadrilateral is divided into 2.

The pentagonal shape is divided into 3 pieces.

The n-sided shape is divided into n-2.

Because the inner angle of each triangle is 180 degrees, the relationship between the inner angle of the polygon and the number of its sides is (n-2)*180 degrees.

1. Definition: The sum of the inner angles of the polygon theorem: the sum of the internal angles of the n-sided is equal to: (n - 2) 180° (n is greater than or equal to 3).

2. Relationship: Sum of internal angles = (number of sides - 2) 180 degrees.

It can be calculated from the triangle inner angle sum (from one vertex to each other vertex separately into n-2 triangles).

n denotes the number of edges.

3. For example, if you know that each inner angle of a polygon is 135°, find the solution of the number of sides of this polygon: (n - 2) 180°=135n, n=8, that is, the number of sides is 8

If it's a regular polygon.

Their internal angles and relation to the number of sides are.

The sum of the internal angles of a regular polygon.

180°×（n-2)

n is a positive integer and greater than 2

n is the number of sides of a regular polygon.

Think of it this way.

First of all, we know that the sum of the internal angles of a triangle is 180

So how many triangles can an n-sided be divided into? There are (n-2) in total, so the inner angles of the n-sided are sum.

It's 180 (n-2).

Sum of internal angles = (number of sides - 2) 180 degrees.

A closed figure composed of three or more line segments on the same plane and not on the same straight line that are connected one after the other and do not intersect is called a polygon. A figure composed of multiple line segments on different planes that are connected sequentially and do not intersect is also called a polygon, which is a polygon in a generalized sense. Polygons have an infinite number of axes of symmetry.

Triangles connect diagonals The triangle is divided into 1.

The quadrilateral is divided into 2.

The pentagonal shape is divided into 3 pieces.

The n-sided shape is divided into n-2.

Because the inner angle of each triangle is 180 degrees, the relationship between the inner angle of the polygon and the number of its sides is (n-2)*180 degrees roy

Answer: The sum of the inner angles of the polygon = (number of sides - 2) * 180°

If the polygon is a convex polygon with n sides, then its internal angles and the relationship to its number of sides are:

The sum of the internal angles = (n-1) 180 degrees.

For example, the sum of the internal angles of a triangle is equal to 180 degrees.

The sum of the internal angles of the quadrilateral is equal to 360 degrees.

The sum of the inner angles of a convex pentagon is equal to 540 degrees.

Since n triangles can be made along the center, the sum of the inner angles of all triangles is n*180, and the sum of the inner angles of the polygon is subtracted by 360 degrees.

1.The sum of the inner angles of the polygon, equal to the number of sides -2, and then 180 degrees, can be calculated.

The inner angle of the polygon and the relationship to the number of its sides: (n-2)x180

The sum of the inside angles of a polygon is the number of its sides minus 2 and multiplied by 180.

The sum of the inner angles of a polygon = (its number of sides 2) x180

Sum of the inner angles of the polygon = (number of sides - 2) x 180