When I try that code on an image on my mac it's nice and smooth. I'm going to assume you are working on a mobile app.
First thing to say is that the image rotation is calculated on the fly. That means that every time you set the able of the image, LiveCode is recalculating all the pixels of the image which is quite expensive. On desktops, you have a pretty powerful CPU so spinning an image is fairly easily handled and looks smooth, but mobile devices have less powerful CPUs and struggle with this operation.
POSSIBLE SOLUTION 1 - LiveCode takes into account the "resizeQuality" property of the image. You can set this to "normal", "good" and "best", the fastest being "normal" which produces a blocky image and the slowest being "best" which has a much higher quality. If you are working with the higher quality settings you can improve performance by temporarily reducing the quality while the rotation is taking place.
on mouseUp
put random(360) into i
set the resizeQuality of image 1 to "normal"
repeat with x=0 to i
set the angle of image 1 to the angle of image 1 + 1
wait for 10 milliseconds
end repeat
lock screen
set the resizeQuality of image 1 to "best"
set the angle of image 1 to the angle of image 1 + 1
set the angle of image 1 to the angle of image 1 - 1
unlock screen
end mouseUp
Notice that to get the image to redraw in high quality I've altered the angle again.
POSSIBLE SOLUTION 2 - If you can't get enough performance from that, the best thing to do would be to generate images for your wheel at all 360 positions. You can then set the filename properly of the image to the correct one.
local tImagesPath
set the itemdel to "/"
put item 1 to -2 of the filename of this stack & slash & "wheel_images" & slash into tImagesPath
set the resizeQuality of image 1 to "best"
repeat with x=0 to 359
set the angle of image 1 to x
export snapshot from image 1 to file tImagesPath & x & ".png" as png
wait 1 millisecond with messages
end repeat
That script generates high quality images of the wheel in 359 positions.
To get good performance on mobile, when you open the app, repeat through all the images of the wheel in 359 positions and call:
prepare image
That will cause LiveCode to preload the image into memory making it possible to render some really smooth animations.