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

You are watching: What is the sum of the interior angles of a nonagon ## Nonagon classifications

Like various other polygons, a nonagon can be share as continuous or irregular. If every the sides and also interior angles of a nonagon space equal, the is a consistent nonagon. Otherwise that is an rarely often rare nonagon.

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

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

Convex nonagonConcave nonagon All internal angles 180°

## Diagonals that nonagon

A diagonal line is a line segment joining two non-consecutive vertices. A total of twenty-seven distinctive diagonals have the right to be drawn for a nonagon. The following figure is an example. There space 6 diagonals expanding from each of the 9 vertices of the nonagon over creating a total of 27 diagonals.

## Internal angles of a nonagon

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

## Regular nonagon

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

### Angles of a continual nonagon

Since every of the nine internal angles in a regular nonagon are equal in measure, each interior angle steps 1260° ÷ 9 = 140°, as displayed below. Each exterior angle of a regular nonagon has actually an equal measure the 40°. ### Symmetry in a continual nonagon

A consistent nonagon has actually 9 currently of symmetry and also a rotational the opposite of bespeak 9, an interpretation that it can be rotated in together a means that it will certainly look the same as the original shape 9 times in 360°.

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