What Is a Pentagon?

What the five-sided count tells you

A regular pentagon has strong symmetry and a fixed interior angle of one hundred eight degrees at each vertex. In a general pentagon, the angle measures may vary, but the total interior angle sum remains five hundred forty degrees.

Pentagons are useful because they introduce side-count naming while also showing that naming and regularity are separate ideas. You name the polygon first and then describe whether it is regular or irregular.

If a five-sided figure has one inward corner, it is still a pentagon because the side count has not changed; it is simply concave. If all five sides and angles match, it is a regular pentagon. These extra adjectives add information after the basic name rather than replacing it.

A regular pentagon has five equal central turns, each 72 degrees, and five equal interior angles of 108 degrees. A general pentagon keeps the 540-degree total even when those individual angles are no longer equal.

A pentagon's name does not promise a particular picture. It may be narrow, wide, regular, irregular, convex, or concave. The five-edge count is the starting fact, and the other adjectives tell you what extra structure the particular example has.

• A pentagon is a polygon with five sides.
• A pentagon always has five sides and five vertices.
• The interior angle sum of any pentagon is five hundred forty degrees.
• A regular pentagon has five equal sides and five equal interior angles of one hundred eight degrees.

Where pentagons help

• Use pentagon naming when classifying polygons by side count.
• Use regular-pentagon facts in angle and symmetry problems.
• Use pentagons as examples when introducing general polygon formulas.

Pentagon checks to make

• Do not confuse five sides with five angles as separate counts; a pentagon has both because it has five vertices.
• Do not treat regular pentagon facts as though they apply to every pentagon.
• Do not miscount the boundary when the polygon is concave or irregular.