# Decagon — Sides, Shapes, Angles, & Definition Written by
Malcolm McKinsey
Fact-checked by
Paul Mazzola

## Decagons definition

decagon is a 10-sided polygon, with 10 interior angles, and 10 vertices which is where the sides meet. Polygons get their name from Greek, meaning "many-angled," because all polygons have multiple interior angles. They close in a two-dimensional space using only straight sides.

### Properties of decagons

For a polygon to be a decagon, it must have these identifying properties:

1. 10 sides

2. 10 interior angles

3. 10 vertices

## Decagon angles

In many decagons, the sum of interior angles will be 1,440°, but that is not an identifying property because complex decagons will not have that sum.

Regular decagons have two additional identifying properties:

1. 10 exterior angles of 36°, summing to 360°

2. 10 interior angles of 144°, summing to 1,440°

Drawing a decagon takes no skill; simply draw 10 line segments that connect, and you have it. Drawing a regular, convex decagon, however, takes real skill, since each interior angle must be 144°, and all sides must be equal in length.

Drawing a concave decagon is actually fairly easy: make a five-pointed star and fill it in. That is the star that appears 50 times on the Unites States flag, and the outline of such a pentagram (five-pointed star) is a decagon.

## Types of decagons

• A decagon is a 10-sided polygon, with 10 interior angles, and 10 vertices which is where the sides meet.

• A regular decagon has 10 equal-length sides and equal-measure interior angles. Each angle measures 144° and they all add up to 1,440°.

• An irregular decagon has sides and angles that are not all equal or congruent.

• A convex decagon bulges outward, with no interior angle greater than 180°.

• A concave decagon have indentations, creating interior angles greater than 180°.

• A simple decagon does not have any sides that cross or intersect.

• A complex decagon has self-intersecting sides, is complex, and highly irregular.

### Regular and irregular decagons

All polygons can be drawn as regular (equal-length sides, equal-measure interior angles) or irregular (not restricted to congruent angles or sides). The regular, convex decagon is a subtle and elegant shape, with 10 exterior angles of 36°, 10 interior angles of 144°, and 10 vertices (intersections of sides).

Because it is a challenging shape to make, the regular, convex decagon is popular with coins (like those from Australia, Belize and Hong Kong). Irregular decagons must simply have 10 sides closing in a space, but the lengths of their sides can vary greatly.

### Concave and convex decagons

Most polygons can be convex or concave. Convex decagons bulge outward, with no interior angle greater than 180°. Concave decagons have indentations, creating interior angles greater than 180°. That is why the outline of a five-pointed star is a concave decagon; it has five interior angles each of which is far greater than 180°.

So far all the decagons discussed - regular, irregular, concave, and convex - share the same properties:

• 10 sides

• 10 vertices

• 10 interior angles

### Simple and complex decagons

Decagons can be simple or complex. A simple decagon has no sides crossing themselves. A simple decagon follows all the conventional "rules" of polygons.