document.write( "Question 1203593: George took out a piece of paper and placed it on his desk. He then drew a polygon. All the angles in the polygon were obtuse. What type of polygon could could he have drawn?\r
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\n" ); document.write( "\n" ); document.write( "I need to know how to determine this answer (hexagon). \n" ); document.write( "
Algebra.Com's Answer #839261 by math_helper(2461)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Using formal Algebra, you can use the sum of interior angles formula:
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document.write( "    S = (n - 2)*180 
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document.write( "where   S = sum of interior angles
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document.write( "        n = number of sides\r
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document.write( " [ You can remember this formula by noting that n-2 is the number
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document.write( "   of non-overlapping triangles you can draw by connecting verticies 
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document.write( "   of an n-sided polygon.  Each triangle having 180 degrees. ]\r
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document.write( "We can compute the average for each of the proposed polygons:
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document.write( "A.  quadrilateral:  4 sides -->  Sum = (4-2)*180 = 360\r
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document.write( "    Since we are told each angle is obtuse, looking at 360/4 = 90, there
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document.write( "    must be some angle that is less than or equal to 90 degrees (allowing
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document.write( "    for irregular quadrilaterals).  Therefore, this can not be the correct
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document.write( "    answer (not all angles can be obtuse). \r
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document.write( "B.  Rectangle:  each angle of a rectangle is 90 degrees, clearly not the correct answer.  This is already covered by A above as well.\r
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document.write( "C. Triangle:  3 sides -->  Sum = (3-2)*180 = 180 degrees,  at most one angle can be obtuse in a triangle, so clearly not the answer.\r
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document.write( "D.  Hexagon:  6 sides:  Sum = (6-2)*180 = 720 degrees.  Since 720/6 = 120, George must have drawn a hexagon (it doesn't have to be a regular hexagon, BUT it can't be any arbitrary hexagon either, as he must've drawn it such that every angle was obtuse).  \r
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document.write( "In summary, the hexagon shape is the only one possible from the choices given.\r
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document.write( "Hope this helps you! \n" );
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