Icosagon — Definition, Formula & Examples

An icosagon is a polygon with 20 sides and 20 vertices. A regular icosagon has all sides equal in length and all interior angles equal.

An icosagon is a closed, simple polygon composed of exactly 20 line segments (sides) meeting at 20 vertices. In its regular form, it exhibits 20-fold rotational symmetry, with each interior angle measuring 162° and each exterior angle measuring 18°.

Key Formula

S = (n - 2) \times 180°

Where:

$S$ = Sum of interior angles of the polygon
$n$ = Number of sides (20 for an icosagon)

Worked Example

Problem: Find each interior angle of a regular icosagon.

Step 1: Use the interior angle sum formula with n = 20.

S = (20 - 2) \times 180° = 18 \times 180° = 3240°

Step 2: Since a regular icosagon has 20 equal angles, divide the sum by 20.

\text{Each angle} = \frac{3240°}{20} = 162°

Answer: Each interior angle of a regular icosagon measures 162°.

Why It Matters

The icosagon appears in geometry courses when students classify polygons by side count and practice angle-sum formulas for any n-gon. Its nearly circular shape also makes it useful for approximating circles in computer graphics and engineering design.

Common Mistakes

Mistake: Confusing an icosagon (20 sides) with a dodecagon (12 sides) or an icosahedron (a 3D solid with 20 triangular faces).

Correction: Remember that the prefix "icosa-" means 20 and refers to sides in 2D. A dodecagon has 12 sides, and an icosahedron is a 3D polyhedron, not a polygon.