document.write( "Question 580179: I know that the equation to find the sum of the measures of the angles for a regular polygon is
\n" ); document.write( "(180)N-360 when N=Number of sides. But I do not understand why.\r
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Algebra.Com's Answer #371194 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "The other tutor said \"Don't argue with what works\".  I agree but\r\n" );
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document.write( "that's not what you did.  You aksed WHY it works, and you are to be\r\n" );
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document.write( "commended for asking that question, not criticized!!!\r\n" );
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document.write( "Here is the answer to your question:  \r\n" );
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document.write( "Any polygon can be divided up into triangles.  The number of triangles\r\n" );
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document.write( "is always two less triangles than the number of sides of the polygon.\r\n" );
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document.write( "For instance, take this 5-sided polygon (called a \"pentagon\", like the buiding \r\n" );
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document.write( "in Washington DC): \r\n" );
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document.write( "If you pick any vertex and draw the diagonals, \r\n" );
document.write( "like this:\r\n" );
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document.write( "the polygon is divided into three triangles (two less\r\n" );
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document.write( "than five).  The interior angles of the 3 triangles are\r\n" );
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document.write( "180° each.   So the sum of the interior angles of the\r\n" );
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document.write( "polygon is 3 times 180°.  That's\r\n" );
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document.write( "the number of sides, 5, minus 2, or 3 times 180°, and if the\r\n" );
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document.write( "number of sides is n, then that's\r\n" );
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document.write( "       (n - 2)180°\r\n" );
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document.write( "But as the other tutor explained, if you use the \r\n" );
document.write( "distributive principle, you get:\r\n" );
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document.write( "     n·180° - 2·180°\r\n" );
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document.write( "and that becomes\r\n" );
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document.write( "      180°n - 360°\r\n" );
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document.write( "Edwin
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