To solve this problem, we need to understand the relationship between the exterior and interior angles of a regular polygon.

- Regular polygon: A polygon is considered regular when all of its sides and angles are equal.

- Interior angle: The interior angle of a polygon is the angle formed inside the polygon at each vertex.

- Exterior angle: The exterior angle of a polygon is the angle formed outside the polygon at each vertex.

Let's assume the interior angle of the polygon is x degrees. According to the given information, the exterior angle is one third of the interior angle. Therefore, the exterior angle can be represented as (1/3)x degrees.

Now, let's consider the sum of the interior angles of a polygon. In any polygon, the sum of the interior angles is given by the formula (n-2) * 180 degrees, where n represents the number of sides of the polygon.

Since the polygon is regular, each interior angle is equal. Therefore, the sum of all interior angles can be represented as n * x degrees.

Using the given relationship between the interior and exterior angles, we can write the equation:

x + (1/3)x = 180

Combining like terms, we get:

(4/3)x = 180

To solve for x, we divide both sides by (4/3):

x = (180 * 3) / 4

x = 135

Now, we can substitute the value of x in the equation for the sum of all interior angles:

n * 135 = (n-2) * 180

Expanding and simplifying, we get:

135n = 180n - 360

Subtracting 135n from both sides:

45n = 360

Dividing both sides by 45:

n = 8

Therefore, the number of sides of the polygon is 8, which corresponds to option D.