The diagram shows part of three regular polygons A, B and C fit together at a common vertex. Polygon A is an icosagon, a 20-sided polygon. [Diagram] What is the special name for polygon B?

1. Find the interior angle of regular polygon A, the 20-sided icosagon.

For a regular $n$-sided polygon,
$\text{interior angle}=\frac{(n-2)\times 180^\circ}{n}.$
For polygon A, $n=20$:
$\text{interior angle of A}=\frac{(20-2)\times 180^\circ}{20}=162^\circ.$

2. Use angles at a point to find the interior angle of polygon B.

The three polygons fit together at a common vertex, so their angles around the point add to $360^\circ$.

The angle for polygon C is marked as a right angle, so it is $90^\circ$.

$\text{interior angle of B}=360^\circ-162^\circ-90^\circ=108^\circ.$

3. Determine the number of sides of polygon B from its interior angle.

Let polygon B have $n$ sides.

$\frac{(n-2)\times 180^\circ}{n}=108^\circ$
$180n-360=108n$
$72n=360$
$n=5.$

4. State the special name of the 5-sided regular polygon.

A polygon with $5$ sides is called a pentagon.