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# How many diagonals does a 9 sided polygon have?

Updated: 10/18/2022

Wiki User

7y ago

A diagonal is a line between two vertices that is not an edge.

As two vertices are connected by an edge, the number of diagonals from a vertex is the number of vertices (or sides or angles) less 3; as each diagonal is counted twice, once for the vertex at each end of it:

number_of_diagonals = ½ × number_of_vertices × (number_of_vertices - 3)

For a nonagon, it has 9 vertices

→ number_of_diagonals = ½ × 9 × (9 -3) = ½ × 9 × 6 = 27.

Wiki User

7y ago

Wiki User

15y ago

Six. Every n-sided polygon has n(n - 3)/2 sides. It has n vertices, and each of the n vertices has a diagonal with each other vertex, except itself and the two that are adjacent to it; hence, it has n - 3 vertices. But, since each diagonal would be thus counted exactly twice, we must divide the n(n - 3) diagonals thus counted, by two. This formula yields zero, for a triangle; two, for a square or other quadrilateral; five, for a pentagon; and nine, for a hexagon; and so, on.

Wiki User

7y ago

A nine-sided polygon, or a nonagon, has 27 diagonals.