The sum of the interior angles of a regular polygon can be calculated using the formula:

Sum of interior angles = (n - 2) 180 degrees

where \(n\) is the number of sides of the polygon.

Given that the sum of the interior angles of the polygon is 1800 degrees, we can set up the equation:

\(1800 = (n - 2) \times 180\)

Solve for \(n\):

\(n - 2 = \frac{1800}{180}\)

\(n - 2 = 10\)

\(n = 12\)

So, the polygon has 12 sides.

The sum of the exterior angles of any polygon is always 360 degrees. In a regular polygon, all exterior angles are congruent, so each exterior angle is:

Size of one exterior angle = Total sum of exterior angles / Number of exterior angles

Size of one exterior angle = 360 degrees / 12

Size of one exterior angle = 30 degrees