Hey! the answer would be A regular 40-sided polygon has an interior angle equal to: (40 - 2) (180) /40 = 171 degrees
The interior angle is also the smallest angle that is needed to rotate the polygon and map it unto itself. So, the smallest degree of rotation needed to map the polygon back to itself is 171 degrees.
Since we need an angle measure we have to use an inverse trig ratio, sin^-1, cos^-1, or tan^-1. Setting up the right triangle we have the opposite and adjacent so we use tan. tan angle = 28/32 tan^-1 (28/32) = 41 degrees
