The exterior angle of a regular polygon is one third of its interior angle. Find the number of sides of the polygon.

Sure, let's solve this step by step.

Step 1: We know that the sum of the interior and exterior angles of a polygon is 180 degrees. Given that the exterior angle is one third of the interior angle, we can set up the equation:

Interior Angle + Exterior Angle = 180 Interior Angle + (1/3)Interior Angle = 180 (4/3)Interior Angle = 180

Step 2: Solve for the Interior Angle:

Interior Angle = (3/4) * 180 = 135 degrees

Step 3: We know that the sum of the interior angles of a polygon is given by the formula (n-2) * 180, where n is the number of sides. So we can set up the equation:

135n = (n-2) * 180

Step 4: Solve for n:

135n = 180n - 360 45n = 360 n = 360 / 45 n = 8

So, the polygon has 8 sides.