A regular polygon is a polygon with all sides and angles equal. The sum of the interior angles of a polygon with $n$ sides (an $n$-gon) is given by the formula:

$\text{Sum of interior angles} = (n-2) \times 180^\circ$

Each interior angle of a regular $n$-gon is:

$\text{Each interior angle} = \frac{(n-2) \times 180^\circ}{n}$

You mentioned that each angle is 180 degrees. Let's substitute this into the formula and solve for $n$:

$180^\circ = \frac{(n-2) \times 180^\circ}{n}$

Dividing both sides by 180 degrees:

$1 = \frac{n-2}{n}$

To solve for $n$, we multiply both sides by $n$:

$n = n - 2$

$0 = -2$

This is a contradiction, meaning there is no regular polygon with each interior angle equal to 180 degrees.

A polygon with angles of 180 degrees doesn't exist because angles of 180 degrees imply a straight line