Geometry

 

1.   At the vertex of a polygon, the sum of the exterior angle and the interior angle is 180^o.   

 

      Since the interior angle is 12 times the exterior angle, the exterior angle has to be 15^o.  

 

      The sum of all exterior angles of a polygon is 360^o, irrespective of the number of sides.  

 

       Therefore, the polygon has 360 / 15 = 24 vertices.   

 

       We shall presuppose that a polygon has the same number of sides as it has vertices,    

 

       Therefore, this polygon has 24 sides.    

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