These could all use the qualifier "regular."
the pentagon is rotation of 72 degrees
Yes, odd phrasing but the regular five sided shape has rotational symmetry when rotated by 360/5=72 degrees. CORRECT
the decagon is rotation of 36 degrees
360/10 = 36. I'd say the regular decagon has 36 degree rotational symmetry. CORRECT
the triangle has a rotation of 180 degrees
An arbitrary triangle may not have any symmetry at all beyond the identity. An equilateral triangle has rotational symmetry by 360/3 = 120 degrees and its multiples; 180 isn't among them; NOT CORRECT.
the octagon has rotation of 32 degrees
The regular octagon (stop sign) has 360/8=45 degree rotational symmetry. NOT CORRECT
the nonagon has rotation of 40 degrees
The regular octagon has 360/9=40 degree rotational symmetry. CORRECT