document.write( "Question 825165: In a regular polygon, the ratio of the measure of an exterior angle to the measure of an interior angle is 2:13. How many sides does the polygon have?\r
\n" ); document.write( "\n" ); document.write( "Thanks in advance. \n" ); document.write( "

Algebra.Com's Answer #497084 by KMST(5328) $\"\"$ $\"About$

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ANOTHER WAY:
\n" ); document.write( "In a polygon with $\"n\"$ sides,
\n" ); document.write( "the sum of the measures of the $\"n\"$ exterior angles is $\"360%5Eo\"$ ,
\n" ); document.write( "and the sum of the $\"n\"$ interior angles is $\"%28n-2%29%2A180%5Eo\"$ .
\n" ); document.write( "If the polygon is a regular polygon, all the exterior angles have the same measure, $\"E\"$ , and all the interior angles have the same measure $\"I\"$ .
\n" ); document.write( "So, for a regular polygon with $\"n\"$ sides,
\n" ); document.write( " $\"n%2AE=360%5Eo\"$ , and $\"n%2AI=%28n-2%29%2A180%5Eo\"$ .
\n" ); document.write( "The ratio is
\n" ); document.write( " $\"n%2AE%2F%28n%2AI%29=360%5Eo%2F%28%28n-2%29%2A180%5Eo%29\"$ .
\n" ); document.write( "Simplifying, we get
\n" ); document.write( " $\"E%2FI=2%2F%28n-2%29\"$ .
\n" ); document.write( "For the polygon of the problem, $\"E%2FI=2%2F13\"$ ,
\n" ); document.write( "so $\"2%2F13=2%2F%28n-2%29\"$
\n" ); document.write( " $\"n-2=13\"$
\n" ); document.write( " $\"n=13%2B2\"$
\n" ); document.write( " $\"highlight%28n=15%29\"$
\n" ); document.write( "
\n" ); document.write( "OR MAYBE:
\n" ); document.write( " $\"360%5Eo%2Fn\"$ : $\"%28n-2%29%2A180%5Eo%2Fn%29%29%29=2%3A13%0D%0A%7B%7B%7B360%5Eo\"$ : $\"%28n-2%29%2A180%5Eo%29%29%29=2%3A13%0D%0A%7B%7B%7B2\"$ : $\"%28n-2%29%29%29%29=2%3A13%0D%0A%7B%7B%7Bn-2=13\"$
\n" ); document.write( " $\"n=13%2B2\"$
\n" ); document.write( " $\"highlight%28n=15%29\"$ \n" ); document.write( "

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