Q: How many diagonals can be drawn from any vertex of a 20 sided polygon?

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7-3 = 4

Two triangles can be formed by the diagonals of one vertex of a four-sided polygon.

47 sides. Take a vertex of an n-sided polygon. There are n-1 other vertices. It is already joined to its 2 neighbours, leaving n-3 other vertices not connected to it. Thus n-3 diagonals can be drawn in from each vertex. For n=50, n-3 = 50-3 = 47 diagonals can be drawn from each vertex. The total number of diagonals in an n-sided polygon would imply n-3 diagonals from each of the n vertices giving n(n-3). However, the diagonal from vertex A to C would be counted twice, once for vertex A and again for vertex C, thus there are half this number of diagonals, namely: number of diagonals in an n-sided polygon = n(n-3)/2.

10 ... any polygon it is 2 less than the number of sides or vertices wince they are the same.

A 5-sided polygon is called a pentagon. You can draw up to 5 diagonals in a pentagon.

Related questions

A diagonal of a polygon is a segment drawn from one vertex to another non-adjacent vertex in a polygon. This leaves 32 diagonals that can be drawn from one vertex in a 35 sided polygon.

It is 18 diagonals

5

In a 54-sided polygon, 53 possible diagonals can be drawn from one vertex to another. These diagonals will not intersect. Therefore, the interior will be divided into 54 regions by the 53 diagonals plus the two sides of the original polygon that adjoin the vertex from which the diagonals are drawn.

98

7-3 = 4

Two triangles can be formed by the diagonals of one vertex of a four-sided polygon.

47 sides. Take a vertex of an n-sided polygon. There are n-1 other vertices. It is already joined to its 2 neighbours, leaving n-3 other vertices not connected to it. Thus n-3 diagonals can be drawn in from each vertex. For n=50, n-3 = 50-3 = 47 diagonals can be drawn from each vertex. The total number of diagonals in an n-sided polygon would imply n-3 diagonals from each of the n vertices giving n(n-3). However, the diagonal from vertex A to C would be counted twice, once for vertex A and again for vertex C, thus there are half this number of diagonals, namely: number of diagonals in an n-sided polygon = n(n-3)/2.

10 ... any polygon it is 2 less than the number of sides or vertices wince they are the same.

36

A 5-sided polygon is called a pentagon. You can draw up to 5 diagonals in a pentagon.

4...