Question 1179357
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How many sides has a regular polygon whose interior angle is 22½
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Having two different answers that contradict each other,  may  PERPLEX  you.


So I came to make things clear to you.



                        Your problem in the post is posed  INCORRECTLY.


<H3>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;There is no a regular polygon with the interior angle of 22 1/2 degrees.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;If the EXTERIOR angle of a regular polygon is 22 1/2 degrees, 

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;then the number of sides (same as the number of vertices) is  {{{360/22.5}}} = 16.</H3>