"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?"
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°
To find out how many degrees are in the central angle of each person's slice of pie, we need to understand that a full circle is 360 degrees.
In this case, the pie is divided into eight equal slices. We know that there is exactly 1/3 of the pie left after distributing one slice to each family member.
To determine the size of each slice, we need to calculate the portion that remains. Since it is given that there is 1/3 of the pie left, we know that 2/3 of the pie has been distributed (8 slices out of 3 equal parts).
Therefore, each slice represents 2/3 of the total pie.
To find out how many degrees each slice represents, we need to calculate the fraction of the total 360-degree circle that corresponds to 2/3.
We can set up a proportion:
2/3 of the pie = x degrees / 360 degrees
Cross-multiplying gives us:
(x degrees) = (2/3) × (360 degrees)
(x degrees) = 240 degrees
Hence, each person's slice of pie represents 240 degrees.