Question

Please help with this rotation

Answer 1

I believe the answer would be the Option A: C

because this figure has 9 sides, each time you rotate to one point, it's 40 degrees. So in order to rotate 140 degrees, you should move 4 times from point to point IN A COUNTER CLOCKWISE DIRECTION.
Doing so, you would land on Point C.

Answer 2

There are nine sides to this polygon. So this is a nonagon. Which also can be written as 9-gon.

So n = 9 and 360/n = 360/9 = 40 is the angle of rotation. We can rotate this nonagon 40 degrees in either clockwise or counterclockwise direction to have it line up with the original nonagon. In other words, the "before" and "after" will be perfectly identical.

Divide the value 160 over the angle of rotation: 160/40 = 4
The result 4 means the nonagon has been rotated four increments of 40 degrees each.

The direction of rotation isn't stated, so we assume the default of counter-clockwise. Point H will rotate to...
point F
point E
point D
point C
each time you bump up another 40 degree rotation increment (four rotations total). Notice how I'm simply moving from point to point along the figure going in a counter-clockwise direction.

So point H will land on point C

Answer: Choice a. C