A nonagon is a polygon that has nine sides. In the figure listed below are several species of nonagons.

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Nonagon classifications

Like various other polygons, a nonagon can be classified as consistent or irregular. If all the sides and interior angle of a nonagon space equal, that is a continuous nonagon. Otherwise the is an irregular nonagon.

Regular nonagonIrregular nonagon
All sides and also interior angles are equalNot all sides and also angles space equal

Nonagons and other polygons can also be classified together either convex or concave. If all inner angles that a nonagon are much less than 180°, it is convex. If one or an ext interior angle is bigger than 180°, that is concave. A continual nonagon is a convex nonagon.

Convex nonagonConcave nonagon
All inner angles 180°

Diagonals that nonagon

A diagonal line is a heat segment joining two non-consecutive vertices. A total of twenty-seven unique diagonals have the right to be drawn for a nonagon. The following figure is one example.


There room 6 diagonals expanding from each of the 9 vertices the the nonagon over creating a total of 27 diagonals.

Internal angles of a nonagon

The amount of the inner angles that a nonagon equals 1260°.


As presented in the figure above, 6 diagonals deserve to be drawn to division the nonagon into seven triangles. The blue lines above show just one method to divide the nonagon into triangles; there room others. The sum of interior angles that the seven triangles equates to the sum of interior angles that the nonagon. Since the amount of the inner angles that a triangle is 180°, the amount of the interior angles of the nonagon is 9 × 180° = 1260°.

Regular nonagon

A continuous nonagon is a nonagon in which every sides have actually equal length and also all internal angles have equal measure.

Angles of a continuous nonagon

Since every of the nine internal angles in a continuous nonagon are equal in measure, each internal angle measures 1260° ÷ 9 = 140°, as displayed below.


Each exterior edge of a continuous nonagon has an equal measure of 40°.


Symmetry in a consistent nonagon

A constant nonagon has 9 currently of symmetry and also a rotational symmetry of stimulate 9, meaning that it can be rotated in such a method that it will certainly look the same as the initial shape 9 time in 360°.

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Lines that symmetryRotational symmetry
9 lines of symmetryNine 40° the rotation about the center.