document.write( "Question 363101: how many degrees are the exterior angles of a 25-gon \n" ); document.write( "
Algebra.Com's Answer #258858 by CharlesG2(834)\"\" \"About 
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\"how many degrees are the exterior angles of a 25-gon\"\r
\n" ); document.write( "\n" ); document.write( "if a regular polygon with all sides equal, then all internal angles will be equal, then also all external angles will be equal\r
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\n" ); document.write( "\n" ); document.write( "25 sides = 25 vertices
\n" ); document.write( "internal angles = (n - 2)*180 = (25 - 2)*180 = 23 * 180 = 4140 degrees
\n" ); document.write( "sum of angles at the vertices = 180n = 180 * 25 = 4500 degrees
\n" ); document.write( "sum external angles = 4500 - 4140 = 360 degrees
\n" ); document.write( "each internal angle = 4140/25 = 165.6 degrees
\n" ); document.write( "each external angle = 180 - 165.6 = 14.4 degrees\r
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\n" ); document.write( "\n" ); document.write( "A polygon with n sides has n - 2 triangles making it up, these triangles are made by drawing non-intersecting diagonals between the vertices (the corners) of the polygon.
\n" ); document.write( "n sides = n-gon = n - 2 triangles,
\n" ); document.write( "internal angles = (n - 2) * 180 = 180n - 360
\n" ); document.write( "n-gon has n vertices
\n" ); document.write( "n * 180 = 180n
\n" ); document.write( "180n - (180n - 360) = 180n - 180n + 360 = 360 = sum of the external angles
\n" ); document.write( "therefore all polygons have 360 degrees as the sum of their external angles\r
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