Each exterior angle of a regular n-gon shaped gazebo at Logan Park measures 22 1/2. Each exterior angle of a regular n-gon shaped gazebo at Cerro Park measures 15 15/23. By how many sides the gazebo at Logan Park is different from the gazebo at Cerro Park?

The difference in number of sides from one park to the next is 7

Step-by-step explanation:

For all polygon's the exterior angles combine to measure to 360 degrees. So to find the number of sides of each gazebo, we simply divide 360 by the measure of each individual exterior angle. We'll start with Logan Park.

360/22.5 = 16 sides

Now we can do the same with Cerro Park.

360/15.65 = 23 sides

Therefore, the difference in sides would be 7

23 - 16 = 7

the exterior angles of a polygon sum to 360

so the number of sides is 360/45

-PlushDna