document.write( "Question 946012: What is the number of sides of a polygon if the sum of the measures of its interior angles is twice the sum of the measures of its exterior angles \n" ); document.write( "

Algebra.Com's Answer #577125 by KMST(5328) $\"\"$ $\"About$

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The sum of the measures of the exterior angles is $\"360%5Eo\"$ >
\n" ); document.write( "(It is so because each exterior angle is the angle that your direction changes at a vertex as you go around the polygon,
\n" ); document.write( "and one turn around the polygon is a $\"360%5Eo\"$ turn).
\n" ); document.write( "If the sum of the measures of a polygon's interior angles is twice the sum of the measures of its exterior angles, then it is
\n" ); document.write( " $\"2%2A360%5Eo=red%28720%5Eo%29\"$
\n" ); document.write( "The sum of the measures of the interior angles of a polygon depends on the number of sides of the polygon, $\"n\"$ ,
\n" ); document.write( "and is $\"green%28%28n-2%29%2A180%5Eo%29\"$ .
\n" ); document.write( "For this problem,
\n" ); document.write( " $\"green%28%28n-2%29%2A180%5Eo%29=red%28720%5Eo%29\"$ ---> $\"n-2=720%5Eo%2F180%5Eo\"$ ---> $\"n-2=4\"$ ---> $\"n=4%2B2\"$ ---> $\"highlight%28n=6%29\"$
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