A. False. Rotating a rectangle 90 degrees won't have it line up with itself unless the rectangle is a square. Non-square rectangles won't work.
B. True. The angle of rotation of a octagon is 45 degrees because 360/n = 360/8 = 45. Think of it as a pie sliced 8 ways with each slice getting 45 degrees.
C. True. Similar to the octagon above, but this time n = 6. So 360/6 = 6. This only works with regular hexagons where all sides are the same length and all angles are the same measure.
D. False. Rotations of 180 degrees for trapezoids aren't guaranteed to have the image line up with the preimage. This will only work for parallelograms, but trapezoids by definition aren't parallelograms as they only have one pair of opposite sides parallel.
E. True. Rotating a parallelogram 180 degrees will have the 'before' and 'after' images looking identical. If you closed your eyes during the transformation, you wouldn't know it took place or not.
-------------------------------------
In summary,
the answers are choice B, choice C, and choice E