Let's break down the problem into a step-by-step process:
1. We start by identifying the sequence of people involved in passing the soup. The soup is initially placed in front of Igor and then passed to Blan, and finally to Abbey.
2. We need to determine the angles of rotation about the center of the table for each pass:
- First, the soup is passed from Igor to Blan.
- Then, the soup is passed from Blan to Abbey.
3. The problem provides us with two possible sets of rotations to consider:
- First [tex]$160^{\circ}$[/tex] and then [tex]$160^{\circ}$[/tex]
- First [tex]$80^{\circ}$[/tex] and then [tex]$80^{\circ}$[/tex]
Given the results, let's move through the steps again:
4. When the soup is passed from Igor to Blan, it rotates about the center of the table by [tex]$80^{\circ}$[/tex].
5. Then, when the soup is passed from Blan to Abbey, it again rotates about the center of the table by [tex]$80^{\circ}$[/tex].
6. The total rotation can therefore be calculated by adding the individual angles of rotation together:
- [tex]$80^{\circ} + $[/tex]80^{\circ}[tex]$ = 160^{\circ}$[/tex]
Thus, the answer to the question is that the soup is passed first by rotating [tex]$80^{\circ}$[/tex] and then by rotating [tex]$80^{\circ}$[/tex]. The combined total rotation amounts to [tex]$160^{\circ}$[/tex].
Therefore, the correct pair of rotations is:
First [tex]$80^{\circ}$[/tex] and then [tex]$80^{\circ}$[/tex].
