document.write( "Question 824774: If one of the interior angles of a polygon is 260° and the remaining interior angles are each 160°,find the number of sides of the polygon. \n" ); document.write( "

Algebra.Com's Answer #496772 by KMST(5328) $\"\"$ $\"About$

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$\"n\"$ = number of sides in the polygon
\n" ); document.write( "The sum of the measures of all interior angles is
\n" ); document.write( " $\"%28n-2%29%2A180%5Eo\"$ .
\n" ); document.write( "So if one interior angle measures $\"260%5Eo\"$ ,
\n" ); document.write( "and the $\"n-1\"$ remaining interior angles measure $\"160%5Eo\"$ each,
\n" ); document.write( "for the sum of all measures in degrees we can write the equation
\n" ); document.write( " $\"260%2B%28n-1%29%2A160=%28n-2%29%2A180\"$
\n" ); document.write( "
\n" ); document.write( "Solving:
\n" ); document.write( " $\"%28n-2%29%2A180=260%2B%28n-1%29%2A160\"$
\n" ); document.write( " $\"180n-360=260%2B160n-160\"$
\n" ); document.write( " $\"180n-160n=260-160%2B360\"$
\n" ); document.write( " $\"20n=460\"$
\n" ); document.write( " $\"n=460%2F20\"$
\n" ); document.write( " $\"highlight%28n=23%29\"$ \n" ); document.write( "

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