In a regular polygon, the interior angle and the exterior angle are in the ratio interior : exterior = 11 : 1�Find the number of sides of this regular polygon�

Step 1: Understand the problem The problem is asking for the number of sides of a regular polygon where the ratio of the interior angle to the exterior angle is 11:1.

Step 2: Use the relationship between interior and exterior angles The sum of the interior angle and the exterior angle of any polygon is 180 degrees. Since the ratio of the interior angle to the exterior angle is 11:1, we can set up the equation 11x + x = 180, where x is the measure of the exterior angle.

Step 3: Solve for x Solving the equation gives x = 180/12 = 15 degrees.

Step 4: Use the relationship between the number of sides and the exterior angle The sum of the exterior angles of any polygon is 360 degrees. Therefore, the number of sides of the polygon is 360 divided by the measure of the exterior angle.

Step 5: Solve for the number of sides 360/15 = 24

So, the regular polygon has 24 sides.