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Nonagon
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05.16 • Polygons

Nonagon

Use this page to read nonagon as a nine-sided polygon and to connect that name with the regular case's one-hundred-forty-degree interior angles.

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⬠ Nonagon
Interactive diagram

Nonagon Diagram

Count the nine sides around the boundary and compare the side-count name with the regular-angle pattern.

Use the movable diagram to see what defines nonagon, how the labels relate to the figure, and what stays true as the board changes.

Definition: A nonagon is a polygon with nine sides.
Detailed definition

Understanding Nonagon

Nonagon is a polygon with nine sides. A nonagon is a polygon with nine sides. Some sources also use the word enneagon, but nonagon is a common classroom name for the same side count.

A regular nonagon has equal sides and equal angles, with each interior angle measuring one hundred forty degrees. Its exterior angles are forty degrees, and the full exterior-angle total still remains three hundred sixty degrees as in every polygon.

This polygon is helpful because it pushes students one step further into systematic polygon naming while still connecting cleanly to the general formulas for n-gons.

Key facts

Important ideas to remember

  • A nonagon is a polygon with nine sides.
  • A nonagon has nine sides and an interior angle sum of one thousand two hundred sixty degrees.
  • Each interior angle of a regular nonagon measures one hundred forty degrees.
  • A regular nonagon has nine equal sides and nine equal angles.
Where it is used

Where nonagon shows up

  • Use nonagon naming when practicing less familiar polygon side counts.
  • Use regular nonagon values in angle and symmetry comparison work.
  • Use the figure to reinforce how named polygons fit under n-gon formulas.
Common mistakes

What to watch out for

  • Do not confuse nonagon with decagon or octagon during fast counting.
  • Do not assume every nonagon is regular just because the example is neatly drawn.
  • Do not forget that side-count naming and regular-angle values are different layers of information.
Worked examples

Nonagon examples

Use these worked examples to see the idea in a clean diagram first, then in the kind of reasoning students usually need for classwork, homework, or test practice.

Example 1

Example 1: Naming a nonagon from its side count

Count the sides and vertices carefully so the polygon name comes from the correct total.

  • Start at one vertex and count around the boundary once.
  • Match the count to the standard polygon name.
  • Check that the shape closes after the final side.

Result: The polygon is named accurately because the side count and vocabulary agree.

Example 2

Example 2: Connecting nonagon to its regular form

Use the same side count to discuss the regular version of the polygon without changing the name itself.

  • Keep the side count fixed.
  • Notice how equal sides and equal angles change the look of the figure.
  • Separate the naming rule from the regularity rule.

Result: The student can name the polygon first and then discuss whether it is regular or irregular.

For

Why this page helps

This page helps because nonagon is less common in everyday geometry language, so a live side-count model makes the name and its regular-case measures easier to retain.

Do

What you can do here

  • Count nine sides and compare the result with the regular nonagon's angle pattern.
  • See how the name stays fixed while the polygon changes between regular and irregular forms.
  • Keep a clean nonagon figure for side-count and formula review.
Learning outcome

What this page helps you do

These takeaways are meant to help you recognize the idea faster, read diagrams more accurately, and use the topic with more confidence in real problems.

1

Nonagon

Name nine-sided polygons with more confidence.

2

Nonagon

Use regular nonagon angle information without losing the basic side-count rule.

3

Nonagon

Strengthen your command of less familiar polygon vocabulary.

05

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An octagon is a polygon with eight sides.

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A decagon is a polygon with ten sides.

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