What is a nonagon?

A nonagon or 9-gon is a nine-sided polygon through nine internal angles that amount to 1260°. A nonagon is also called an enneagon. In countless ways, enneagon is a an ext accurate term, due to the fact that it offers Greek roots because that both that is prefix (ennea-, meaning nine) and also suffix (-gon, angled).

You are watching: Number of diagonals in a nonagon

Nonagons room rarely offered in many geometry texts, yet it is an intriguing shape, even if it is you study a consistent nonagon or an rarely often rare nonagon.

*


Nonagon shape

To be a nonagon or enneagon, the shape must have all this properties:

It must be 2 dimensional (planar)It must use only nine heat segmentsIt need to close in an area

The nine line segments room the nonagons" sides, and they connect to form the nonagons" angles.

*

Nonagon sides

A nonagon has nine right sides of equal length. If the sides room all the very same length, then you have a regular nonagon. If the sides vary in length, climate you have actually an irregular nonagon.

*

If the sides are curved, the is no a nonagon.

Nonagon angles

Every nonagon has actually nine inner angles that amount to 1260°, and also the ripe exterior angles of a nonagon sum to 360°.

*

Every an easy nonagon (not complex) can have it"s interior separated into seven triangles.

*

You can discover the sum of internal angles by multiplying 7 × 180°, which is just how you gain 1260°.

Nonagon diagonals

Because every diagonal has actually 9 internal angles that connect, a nonagon has actually 27 diagonals.

*

Regular nonagon

A regular nonagon shape has 9 same sides and also 9 congruent angles. In a continuous nonagon, each interior angle procedures 140°.

A regular nonagon is a subtle and also beautiful design:

*

It is very nearly a circle, but not quite. The inner angles are each 140°. You have the right to verify this since 1260° ÷ 9 (angles) = 140°.

The central angle is 40° (which you can calculate by separating 360° by 9). This way you have the right to construct a constant nonagon through 7 isosceles triangles through two angle of 70° and one edge of 40°.

See more: Cadillac Trunk Pull Down Motor Fuse ? Deville Trunk Pull Down Not Working

Irregular nonagon

Irregular nonagons have the right to have sides of different lengths and also interior angle of varying sizes. Yet, also odd shapes like these room nonagons:

*

A polygon v at least one internal angle higher than 180° is a concave polygon and constantly created an rarely often rare polygon.