SOLUTION: If a 75-degree sector rotates around the center of a circle in 75-degree movements, howmnay sector movements will be needed for the sector to land in its original position?

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Question 134324: If a 75-degree sector rotates around the center of a circle in 75-degree movements, howmnay sector movements will be needed for the sector to land in its original position?
Found 2 solutions by scott8148, josmiceli:
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
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, 24 steps

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
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