A regular decagon has 10 sides. The central angle is equally divided into 10, which is 360/10=36 ° between adjacent diagonals.
This also means that a rotation of 36 ° will create an image identical to the preimage, except for letter labels. The order of rotational symmetry is therefore 10, with angles of rotations in multiples of 36 ° .
Thus, A' coincides with B, the rotation angle is 36 °. If A' coincides with C, the rotation is 36*2=72 ° and so on.
So the number of letter spaces between A and the destination letter, multiplied by 36 ° gives the rotation angle, in this case, clockwise, since this is how the letters are numbered.
Back to the question,
Vertex letter spaces angle
D 3 * 36=108 °
F 5 * 36=180 °
H 7 * 36=252 °
I 8 * 36=288 °