Final answer:
The ratio of the interior angle to the exterior angle of a regular polygon is 5:2, which allows us to find that the polygon is a heptagon with 7 sides.
Step-by-step explanation:
The ratio of the interior angle to the exterior angle of a regular polygon is given as 5:2. To find the number of sides of the polygon, we need to know the relationship between an interior angle A and exterior angle E of a regular polygon, which is A + E = 180 degrees (since they are supplementary angles).
Given the ratio A:E = 5:2, let's assume 5x for the interior angle and 2x for the exterior angle. This leads us to 5x + 2x = 180. Solving for x, we get x = 180/7 degrees. Since we know that an exterior angle of a regular polygon is 360/n degrees, where n is the number of sides, we get 2x = 360/n.
Substituting for x, we have (360/7) = 360/n. Simplifying this equation gives us n = 7, which means the polygon has 7 sides. The polygon is therefore a heptagon.