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

You are watching: Interior angles of a regular nonagon


Nonagon classifications

Like various other polygons, a nonagon deserve to be classified as constant or irregular. If every the sides and interior angles of a nonagon room equal, it is a regular nonagon. Otherwise that is an irregular nonagon.

Regular nonagonIrregular nonagon
All sides and interior angles room equalNot every sides and angles space equal

Nonagons and also other polygon can also be classified together either convex or concave. If all interior angles the a nonagon are less than 180°, the is convex. If one or much more interior angles is larger than 180°, it is concave. A constant nonagon is a convex nonagon.

Convex nonagonConcave nonagon
All internal angles 180°

Diagonals that nonagon

A diagonal line is a heat segment joining 2 non-consecutive vertices. A full of twenty-seven distinctive diagonals have the right to be attracted for a nonagon. The following figure is an example.


There room 6 diagonals extending from each of the 9 vertices of the nonagon above creating a complete of 27 diagonals.

Internal angle of a nonagon

The amount of the internal angles the a nonagon equals 1260°.


As shown in the number above, six diagonals can be attracted to divide the nonagon into seven triangles. The blue lines above show just one way to division the nonagon into triangles; there space others. The sum of internal angles of the 7 triangles amounts to the sum of inner angles that the nonagon. Because the sum of the inner angles the a triangle is 180°, the amount of the internal angles the the nonagon is 9 × 180° = 1260°.

Regular nonagon

A regular nonagon is a nonagon in which every sides have equal length and also all inner angles have equal measure.

Angles that a regular nonagon

Since every of the nine interior angles in a regular nonagon space equal in measure, each interior angle procedures 1260° ÷ 9 = 140°, as shown below.


Each exterior angle of a consistent nonagon has actually an equal measure of 40°.


Symmetry in a consistent nonagon

A constant nonagon has 9 lines of symmetry and also a rotational symmetry of stimulate 9, an interpretation that it deserve to be rotated in together a way that it will look the exact same as the initial shape 9 times in 360°.

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