The sum of the interior angle of a regular polygon is 1800o. Calculate the size of one exterior angle of the polygon

The sum of the interior angles of a polygon with n sides is given by the formula (n-2) x 180 degrees. Since the polygon in this question is regular, all its interior angles are equal, and therefore each interior angle of this polygon measures (n-2) x 180 degrees / n. To find the size of one exterior angle, we can use the fact that the sum of the exterior angles of any polygon is always 360 degrees. Therefore, each exterior angle of this polygon measures 360 degrees / n. Using the fact that the sum of the interior angles of the polygon is 1800 degrees, we can write: (n-2) x 180 degrees = 1800 degrees Solving for n, we get n=12. Therefore, the polygon has 12 sides. Using the formula for the exterior angle of a regular polygon, we can calculate the size of one exterior angle: 360 degrees / 12 = 30 degrees. Therefore, the size of one exterior angle of the polygon is 30 degrees.