Question

find the number of sides of a regular polygon if each of its interior angle is 144 degree

Answer 1

The sum of the measures of the interior angles of a polygon with n sides is: (n - 2)* 180degrees. 

Since the polygon has n sides, each interior angle measures (n - 2)*180degrees/n. 

144 = (n - 2)*180/n 
144n = (n - 2)*180 
144n = 180n - 360 
360 = 36n 
---------------------- 
[ n = 10 sides ] 

Answer 2

The sum of the measures of the interior angles of a polygon with n sides is: (n - 2)* 180degrees.  

Since the polygon has n sides, each interior angle measures (n - 2)*180degrees/n.  

144 = (n - 2)*180/n  

144n = (n - 2)*180  

144n = 180n - 360  

360 = 36n  

n = 10 sides