What Is a Decagon?

The ten-sided pattern

A regular decagon has equal sides and equal interior angles of one hundred forty-four degrees. Its exterior angles are thirty-six degrees, which connects it nicely to pentagon-based angle patterns in the regular case.

This polygon is useful because the ten-side count leads to rich but still manageable combinatorial facts such as many diagonals and a large interior angle sum, while staying close to familiar decimal counting.

A regular decagon can be understood by dividing one full turn at the center into ten equal pieces. Each outside turn is 36 degrees, and the inside angle is the supplement of that turn. This gives a reason for the numbers instead of leaving them as isolated facts to memorise.

The ten-sided boundary also has 35 diagonals, found by choosing vertices and removing the sides and repeated endpoints from the count. You do not need this number to name a decagon, but it shows how much more structure appears as side count grows.

The regular decagon's interior angle of 144 degrees leaves a 36-degree outside turn at each corner. Adding those ten equal outside turns returns to one full 360-degree rotation, which is a clean check on the angle values.

• A decagon is a polygon with ten sides.
• A decagon has ten sides, ten vertices, and an interior angle sum of one thousand four hundred forty degrees.
• Each interior angle of a regular decagon measures one hundred forty-four degrees.
• A decagon has thirty-five diagonals in total.

Where decagons are useful

• Use decagon naming in polygon classification and side-count exercises.
• Use regular-decagon angles in symmetry and angle-measure problems.
• Use the shape to compare polygon diagonals and interior sums across different side counts.

Decagon checks to make

• Do not mix the regular decagon's angle values into irregular decagon cases automatically.
• Do not lose count in a shape with many short sides and many diagonals.
• Do not confuse ten sides with ten diagonals; those are different counts entirely.