Let's assume the measure of each exterior angle of the regular polygon is
.
According to the given information, the measure of each interior angle is three times the measure of each exterior angle. Therefore, the measure of each interior angle is
.
In a regular polygon, the sum of all interior angles is given by the formula
, where
is the number of sides of the polygon.
Since each interior angle measures
, the sum of all interior angles can also be expressed as
.
Setting these two expressions equal to each other, we can write the equation:

Now, we can solve for
, the number of sides of the polygon.
Dividing both sides of the equation by
:

Simplifying:

This equation shows that the number of sides
is proportional to
. We need more information, specifically the value of
, to determine the exact number of sides of the polygon.