document.write( "Question 1132033: The interior angles of a convex nonagon have degree measures that are integers in arithmetic sequence. What is the smallest angle possible in this nonagon? \n" ); document.write( "

Algebra.Com's Answer #748872 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "The sum of the interior angles of a nonagon is 180(9-2) = 1260. The average measure of an angle is 1260/9 = 140.

\n" ); document.write( "Since the measures of the nine angles are in arithmetic sequence, the smallest is 140-4n and the largest is 140+4n, where n is the common difference between the angle measures.

\n" ); document.write( "For the polygon to be convex, the largest angle has to be less than 180 degrees:

\n" ); document.write( " $\"140%2B4n+%3C+180\"$
\n" ); document.write( " $\"4n+%3C+40\"$
\n" ); document.write( " $\"n+%3C+10\"$

\n" ); document.write( "Since the angle measures are integers, n=9, and the measure of the smallest angle is 140-4n = 140-4(9) = 104 degrees. \n" ); document.write( "

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