Calculate the number of sides of a regular polygon, if its interior angle is 5 times its exterior angle.

Sure, let's solve this step by step:

1. We know that the interior angle (I) is 5 times the exterior angle (E). So, we can write this relationship as: I = 5E.

2. We also know that the sum of the interior angle and the exterior angle of a polygon is 180 degrees. So, we can write this relationship as: I + E = 180.

3. Now, we can substitute the first equation into the second to solve for E. This gives us: 5E + E = 180, which simplifies to 6E = 180.

4. Solving for E, we get: E = 180 / 6 = 30 degrees.

5. The sum of the exterior angles of any polygon is 360 degrees. So, to find the number of sides (n), we divide 360 by the measure of each exterior angle. This gives us: n = 360 / 30 = 12.

So, the regular polygon has 12 sides.