document.write( "Question 290917: I am a regular polygon with all obtuse angles. i have the smallest number of sides of any polygon with obtuse angles.
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Algebra.Com's Answer #210492 by Edwin McCravy(20060) $\"\"$ $\"About$

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document.write( "The fotmula for the sum of the interior angles of\r\n" );
document.write( "any n-sided polygon is (n-2)*180°, and since\r\n" );
document.write( "a regular polygon has n congruent interior angles,\r\n" );
document.write( "each one has \r\n" );
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document.write( "You can't have 3 sides because a regular 3-sided polygon is an\r\n" );
document.write( "equilateral triangle, which has 60° interior angles.\r\n" );
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document.write( "You can't have 4 sides because a regular 4-sided polygon is a\r\n" );
document.write( "square, which has 90° interior angles.\r\n" );
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document.write( "So you must have 5 sides because a regular pentagon has\r\n" );
document.write( "108° interior angles, and a 108° angle is an obtuse angle.  \r\n" );
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document.write( "Maybe your teacher wants you to do it this way:\r\n" );
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document.write( "Since an obtuse angle is one greater than 90°\r\n" );
document.write( "You could get the answer by the inequality\r\n" );
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document.write( "Multiply through by n.  Since n is positive,\r\n" );
document.write( "we do not reverse the inequality:\r\n" );
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document.write( "So the smallest integer greater than 4 is 5.\r\n" );
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document.write( "Edwin

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