Let's solve this problem together! If the interior angle of a regular polygon doubles its corresponding exterior angle, then the measure of each interior angle is 2 times the measure of each exterior angle. Let's denote the measure of each interior angle by x and the measure of each exterior angle by y. Then, we have x = 2y. Since the interior and exterior angles are supplementary, we also have x + y = 180°. Substituting x = 2y into this equation, we get 2y + y = 180°, which simplifies to 3y = 180°. Solving for y, we find that y = 60°. Since the sum of the exterior angles of any polygon is 360°, the number of sides of the polygon is 360° / y = 360° / 60° = 6. So, the polygon has 6 sides.