What Is a Nonagon?

What changes in the regular case

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.

The word nonagon is easier to remember when you say the count aloud as you trace the border: one through nine, then back to the starting point. Once the count is secure, you can add whether the shape is regular, convex, or concave without mixing those descriptions together.

A regular nonagon also has 27 diagonals. That count is another reminder that a polygon's boundary and its interior connections carry different information. Naming the shape needs only nine sides; diagonal questions need a second piece of reasoning.

A nonagon's name remains stable even if the shape is stretched or its vertices move, provided the boundary stays closed and has nine sides. Regular-angle facts should be restored only when the side and angle equality returns.

• 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 nonagons fit

• 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.

Nonagon checks to make

• 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.