document.write( "Question 225075: How can you find the sum of the interior angles of the points of a 5 point star made out of three triangles, but forming a polygon? There are no equilateral triangles and no right angles. \n" ); document.write( "
Algebra.Com's Answer #168073 by Edwin McCravy(20056)\"\" \"About 
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How can you find the sum of the interior angles of the points of a 5 point star made out of three triangles, but forming a polygon? There are no equilateral triangles and no right angles.
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document.write( "I'm not sure what you mean.  Here's a 5-pointed star, but I don't\r\n" );
document.write( "know how to make a 5-pointed star out of three triangles.\r\n" );
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document.write( "Did you mean this kind of 5-pointed star, also known as a pentagram?  \r\n" );
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document.write( "If so, we'll extend the lines like this:\r\n" );
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document.write( "In the center is a 5-sided regular polygon (a regular\r\n" );
document.write( "pentagon).  The sum of the interior angles of a polygon\r\n" );
document.write( "is gotten by the formula:\r\n" );
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document.write( "SUM OF INTERIOR ANGLES = (NUMBER OF SIDES - 2) * 180°\r\n" );
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document.write( "For a 5-sided polygon (pentagon) this is (5-2)*180° = 3*180°=540°\r\n" );
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document.write( "Since all 5 angles of a regular pentagon are equal, each\r\n" );
document.write( "interior angle of the regular pentagon is \"540%2F5\"° = 108°\r\n" );
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document.write( "So I'll mark one of the 108° interior angles of the pentagon:\r\n" );
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document.write( "Its suppplement is found by subtracting 180°-108°=72°.\r\n" );
document.write( "We'll mark it 72°:\r\n" );
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document.write( "That 72° angle is one of the base angles of an isosceles\r\n" );
document.write( "triangle.  So we'll mark the other base angle 72° also.\r\n" );
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document.write( "Now we can find the angle at the top point of the star by\r\n" );
document.write( "adding the two equal base angles and subtracting from 180°.\r\n" );
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document.write( "72° + 72° = 144°\r\n" );
document.write( "180° - 144° = 36°\r\n" );
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document.write( "So each point of the star is 36°.\r\n" );
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document.write( "You wanted the sum of the points interior angles of \r\n" );
document.write( "the points.  There are 5 of them, so 5 times 36° is\r\n" );
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document.write( "180°.\r\n" );
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document.write( "Edwin
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