The polygon will have 40 sides.
The measure of the interior angles of a polygon is determined by the formula
##((n – 2)180)/n## = interior angle measure
were ##n## is the number of angles and sides of the polygon.
We know that the interior angles of the polygon in the question have measures of ##171^o##
##((n – 2)180)/n = 171^o##
##((n – 2)180) = 171^o(n)##
##180n – 360 = 171n##
## -360 = 171n-180n##
##-360 = -9n##
##-360/-9 = n##
##40 = n##
The polygon will have 40 sides.