in 5 steps, the sector rotates 375°; which puts it 15° out of sync

each additional 5 steps rotates the sector 375° and puts it another 15° out of sync

after 5 rotations (25 steps), the sector is 75° out of sync; which means one step back puts it in sync

so,

If the sector goes around the circle 5 times, the leading edge

will be 5%2A75+-+360+=+15 degrees ahead of where it started

With this position as a starting point, if the sector goes around

the circle 5 more times, the leading edge will now be 30 degrees

ahead of it's starting point.

24%2A15+=+360, so the sector needs to go around the circle

24%2A5+=+120 times to end up back where it started.

its the answer...

Good evening

Have a nice day