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# How many diagonals does a nonagon have?

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A nonagon, or enneagon, is a polygon with nine sides and nine vertices, and it has 27 distinct diagonals. The formula for determining the number of diagonals of an n-sided polygon is n(n - 3)/2; thus, a nonagon has 9(9 - 3)/2 = 9(6)/2 = 54/2 = 27 diagonals.

## Keep Learning

The diagonal of a polygon is any line segment joining two nonadjacent vertices. A nonagon has nine vertices, and each vertex has six other vertices that are not adjacent; thus, each vertex forms six diagonals. For each vertex, there are three fewer diagonals than there are vertices. This is the first part of the procedure for finding the number of diagonals of a polygon: n(n - 3) = 9 x 6 = 54. Each diagonal has two end points, so in order to not count a duplicate diagonal, the final step is to divide 54 by 2, which results in 27 diagonals.

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## Related Questions

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A person draws a hexagon by drawing a closed polygon with six sides and six vertices. A regular hexagon has six equal sides and six equal angles. A person can draw a regular hexagon using a geometric construction.

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The polygon with 1,000 sides, 1,000 vertices and 1,000 angles is called a chiliagon or a 1,000-gon. The term "chiliagon," with a Greek-derived prefix meaning “thousand,” is a proposed name for the 1,000-sided, two-dimensional shape, but it is seldom used.

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A nine-sided shape is called a nonagon or enneagon. A nonagon is a type of polygon. Polygons are closed-plane figures that are made of line segments.