Question 1117557
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If the interior angle is of 175 degrees, then the exterior angle (which is supplement to the interior angle) is of 5 degrees.


The sum of all exterior angles of any (regular) polygon is 360 degrees,


so the number of vertices of the given polygon is  {{{360/5}}} = 72,


and the number of sides is 72, too.
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Answered and solved.