Regular Shapes: All About Nonagons

What are Nonagons?

If you are reading this, you probably already know that enclosed shapes made up of line segments are referred to as polygons. Depending on the amount of sides they hold, they are given special names. Although there is no official name for a 9-sided polygon, the term "nonagon" is commonly used when talking about nine-sided polygons.

Fun Fact:

  • You can also write it as a 9-gon

Quick Overview of Nonagons

Property
Info
 
Sum of Angles
1260 degrees
 
Interior Angle
140 degrees
 
Exterior Angle
40 degrees
 
Nonagon sides
9 sides
 
Central Angle
40 degrees
 

Regular Nonagon

A regular nonagon
A regular nonagon | Source

Nonagon Interior Angles

If you recall, an interior angle is an angle inside a shape. For irregular nonagon (where sides are not equal and therefore those nonagon angles are not equal), there is no way to just know what the interior angle of a nonagon is other than to actually do some measuring.

But for regular nonagons, all of the nonagon interior angles have the same size: 140 degrees

How do I know this?

  • The total sum of angles within a polygon can be acquired by the formula (sides - 2) * 180.
  • For nonagons, this would be: (9-2) * 180 or 1260 degrees.
  • The sum of interior angles of a nonagon is therefore 1260 degrees.
  • So if the sum of interior angles of a nonagon is 1260, and there are 9 angles, then 1260/9 gives you the size of each angle in regular nonagons. 1260 / 9 is 140 degrees!

Exterior Angle of a Nonagon

As previously stated, for an irregular nonagon, there would be no way to know what the interior - and therefore exterior - angles are without doing some measuring. But for a regular one, it's really not that hard!

Exterior angles are supplementary (which means interior + exterior = 180 degrees). So if the interior angle is 140 degrees, the exterior angle of a nonagon has to be 40 degrees. 

Note: If you're doing the angle out of 360, it'd be 220 degrees. However, it's not generally proper to do exterior angles out of 360, even though you could draw a circle around it....

Central Angle of a Regular Nonagon

Since a regular nonagon has equal sides, the diagonals from the origin to the vertices have equal distance between them. What I mean is that there is an equal angle from the line segment that gone from the origin to one of the vertices to another line segment that goes to another vertex.

Since there are 360 degrees around the origin, and there are 9 line segements, each central angle is 360 / 9 = 40 degrees!

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stephanie 2 years ago

thanks so much!

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