Final answer:
This proportion can be calculated as (4x / (1.25 + 5x)) * 360 degrees.
Step-by-step explanation:
The problem states that four times as many children chose tomato soup as chose mushroom soup, so let's assume that the number of children who chose mushroom soup is x. Therefore, the number of children who chose tomato soup is 4x.
Since a quarter of the children chose chicken soup, we can represent this as 1/4 or 0.25. The total number of children surveyed is the sum of the children who chose chicken soup, tomato soup, and mushroom soup, which is 0.25 + 4x + x = 1.25 + 5x.
To find the proportion of children who chose tomato soup, we divide the number of children who chose tomato soup by the total number of children.
So, the proportion is 4x / (1.25 + 5x). The angle for the children who chose tomato soup in the pie chart can be calculated as the proportion multiplied by 360 degrees, because a full circle represents 100% or 360 degrees.
Therefore, the angle for the children who chose tomato soup is (4x / (1.25 + 5x)) * 360 degrees.