"For Thanksgiving dessert, Mrs. Zappone and her seven family members baked an incredible homemade apple pie. Eight equal slices (sectors) of the round pie are cut and one piece is distributed to each person at dinner. After this is done, there is exactly 1/3 of the pie left. How many degrees are in the central angle of each person’s slice of pie?"

Answer 1

This question is misleading.
First, one has to assume that the pie is circular with all the discussion about
sectors etc.
At first I assumed that the pie was cut into 8 equal pieces, as is usually the case and easy to do. Then it said 1/3 of the pie was left after those 8 pieces were distributed, ahhh, there were more than 8 pieces cut, so .....

the 8 pieces represent 2/3 of the pie, making each piece (1/8)(2/3)(360°)
or 30°

That is, they must have cut the pie into 12 pieces, and each piece was a sector with 30°