document.write( "Question 196940: The question is:
\n" ); document.write( "If each interior angle of a regular polygon measures 135°, the polygon must be
\n" ); document.write( "A) octagon
\n" ); document.write( "B) decagon
\n" ); document.write( "C) hexagon
\n" ); document.write( "D) pentagon \n" ); document.write( "

Algebra.Com's Answer #147647 by Edwin McCravy(20056) $\"\"$ $\"About$

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The question is:
\n" ); document.write( "If each interior angle of a regular polygon measures 135°, the polygon must be
\n" ); document.write( "A) octagon
\n" ); document.write( "B) decagon
\n" ); document.write( "C) hexagon
\n" ); document.write( "D) pentagon
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document.write( "Let the number of sides (and angles) of the polygon be n\r\n" );
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document.write( "The formula for the the sum S of the n interior angles\r\n" );
document.write( "of an n-sided polygon is:\r\n" );
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document.write( "S = (n - 2)*180°.\r\n" );
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document.write( "Since the polygon is regular, all its n interior angles\r\n" );
document.write( "are the same.  Therefore the sum of them is (135°) times n,\r\n" );
document.write( "or 135n°\r\n" );
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document.write( "So we also have S = 135n°\r\n" );
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document.write( "So setting equals equal:\r\n" );
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document.write( "(n - 2)*180° = 135n°\r\n" );
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document.write( "(n - 2)*180 = 135n\r\n" );
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document.write( "180(n - 2) = 135n\r\n" );
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document.write( "180n - 360 = 135n\r\n" );
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document.write( "180n - 135n = 360\r\n" );
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document.write( "45n = 360\r\n" );
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document.write( "  n = 8\r\n" );
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document.write( "So the regular polygon has 8 sides and is\r\n" );
document.write( "therefore an octagon.\r\n" );
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document.write( "Edwin

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