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 #701543 by MathTherapy(10557)\"\" \"About 
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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?
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Let the number of sides be n
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document.write( "Sum of INTERIOR angles of ANY POLYGON = 180(n – 2), or 180n - 360\r
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document.write( "The 3 INTERIOR angles measure 160o each, or sum to 3(160), or 480
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document.write( "The REMAINING number of sides = n – 3
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document.write( "The REMAINING INTERIOR angles measure 120o each, or sum to (n - 3)120, or 120n – 360
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document.write( "Sum of the INTERIOR angles of THIS POLYGON = 480 + 120n – 360\r
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document.write( "We then get: 180n – 360 = 480 + 120n - 360
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document.write( "180n - 360 = 120n + 120
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document.write( "180n – 120n = 120 + 360
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document.write( "60n = 480
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document.write( "n, or number of sides = \"highlight_green%28matrix%281%2C4%2C+480%2F60%2C+or%2C+8%2C+%22%28octagon%29%22%29%29\"\r
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document.write( "OR\r
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document.write( "Let the number of sides be S
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document.write( "Since 3 INTERIOR angles measure 160o each, each corresponding exterior angle measures 20o 
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document.write( "Total measure of the 3 corresponding EXTERIOR angles is: 3(20), or 60o  
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document.write( "Number of OTHER sides: S - 3
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document.write( "Since the other INTERIOR angles measure 120o  each, each of the OTHER corresponding exterior angles measures 60o (180 – 120)
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document.write( "Total measure of the OTHER corresponding EXTERIOR angles is: (S - 3)60, or 60S - 180\r
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document.write( "With the SUM of the EXTERIOR angles of a polygon being 360o , we get: 60 + 60S – 180 = 360
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document.write( "60S – 120 = 360
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document.write( "60S = 360 + 120
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document.write( "60S = 480
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document.write( "n, or number of sides = \"highlight_green%28matrix%281%2C4%2C+480%2F60%2C+or%2C+8%2C+%22%28octagon%29%22%29%29\"
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document.write( "ACCEPT no other answer. \n" );
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