Question 1118114
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The sum of the measures of an interior angle and the corresponding exterior angle is 180 degrees.  So the exterior angles of the polygon form the arithmetic sequence 8, 16, 24, ....<br>
The sum of the exterior angles of any polygon is 360.  So<br>
8+16+24+...+8n = 360<br>
The sum of an arithmetic sequence is the number of terms, multiplied by the average of all the terms, which is the same as the average of the first and last terms:<br>
{{{n((8+8n)/2) = 360}}}
{{{n(8+8n) = 720}}}
{{{n(n+1) = 90}}}<br>
By inspection, n = 9<br>
The polygon has 9 sides.