What Is an Octagon?

Octagon facts from the boundary

A regular octagon has especially memorable angle behavior: each interior angle is one hundred thirty-five degrees, and each exterior angle is forty-five degrees. Because the side count is even, opposite sides in the regular case are parallel.

Octagons are useful because they show how named polygons can carry both a simple counting rule and a richer set of regular-case properties when symmetry is added.

A regular octagon can be split into eight equal central wedges. That makes the 45-degree exterior turn easy to picture, while the 135-degree interior angle is the amount left inside each corner. An irregular octagon keeps the eight-side name but does not keep those equal measures.

The word octagon tells you there are eight sides, eight vertices, and an interior-angle total of 1,080 degrees. Regularity adds equal measurements later. This order of reasoning works even when the drawing is rotated or not perfectly neat.

An octagon is also a good example of why visual familiarity can mislead. A stop-sign outline is regular, but a hand-drawn eight-sided boundary may not be. Count the edges first, then inspect the measurements.

• An octagon is a polygon with eight sides.
• An octagon has eight sides, eight vertices, and an interior angle sum of one thousand eighty degrees.
• Each interior angle of a regular octagon measures one hundred thirty-five degrees.
• In a regular octagon, opposite sides are parallel.

Where octagons help

• Use octagon naming in side-count and polygon-classification work.
• Use regular-octagon facts in angle, symmetry, and design-related geometry problems.
• Use octagons to compare even-sided polygon behavior with odd-sided polygon behavior.

Octagon checks to make

• Do not confuse the regular octagon's angle values with the angles of every octagon.
• Do not lose the side count in a highly symmetric or nearly circular-looking regular case.
• Do not mix octagon with decagon just because both have many sides.