document.write( "Question 1087233: three interior angles of a polygon are 160degres each.if the other interior angles are 120degres each,find the number of sides of the polygon? \n" ); document.write( "

Algebra.Com's Answer #701519 by rothauserc(4718) $\"\"$ $\"About$

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each time we add a side to a polygon we add 180 degrees
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\n" ); document.write( "for example, 3 sides = 180, 4 sides = 360, 5 sides = 540, 6 sides = 720, ....
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\n" ); document.write( "we are given that 3 interior angles are 160 degrees each and the rest are 120 degrees each
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\n" ); document.write( "let the sum of the interior angles of our polygon be n, then
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\n" ); document.write( "120 must divide (n - 3 * 160)
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\n" ); document.write( "we see that a polygon with 6 sides is 720 and (720 - 480) = 240 which is divisible by 120
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\n" ); document.write( "furthermore 8 sided polygon is 1080 and (1080 - 480) = 600 which is divisible by 120
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\n" ); document.write( "now we can establish a pattern
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\n" ); document.write( "Beginning with polygons with 6 sides, we have the sequence 6, 8, 10, 12, ... sided polygons that satisfy the criteria
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