document.write( "Question 258750: If the number of sides of an n-sided regular polygon is increased by 4, each
\n" ); document.write( "interior angle is increased by 32°. How many sides are in the newly formed
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Algebra.Com's Answer #190468 by Alan3354(69443)\"\" \"About 
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If the number of sides of an n-sided regular polygon is increased by 4, each
\n" ); document.write( "interior angle is increased by 32°. How many sides are in the newly formed
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\n" ); document.write( "Use the exterior angles, it's simpler.
\n" ); document.write( "Each exterior angle is decreased by 32 degs.
\n" ); document.write( "ext angle = 360/n
\n" ); document.write( "360/(n+4) = (360/n) - 32 = (360 - 32n)/n
\n" ); document.write( "cross multiply
\n" ); document.write( "360n = (n+4)*(360-32n) = -32n^2 + 232n + 1440
\n" ); document.write( "90n = -8n^2 + 58n + 360
\n" ); document.write( "8n^2 + 32n - 360 = 0
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\n" ); document.write( "n = -9 ignore
\n" ); document.write( "n = 5
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\n" ); document.write( "The original polygon has 5 sides. Increasing to 9 sides adds 32 degs to each interior angle.\r
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