Answer:
The angle from the centre of Ann's slice is 60 degrees.
Explanation:
If the size of the slices is proportional to the ages of the children eating the cake, then the sum of their ages equal to 360 degrees (since the cake is a circle).
So to work out the angle of Ann's portion, we find a fraction for Ann's age over the total of all of their ages. So:
5/(5 + 10 + 15) = 5/30
Now since we know their ages are proportional to the slices of cake, we can find the same value for the fraction 5/30 that is out of 360 to work out the angle. Let's call the angle representing Ann's slice x. So know we can create an equation:
5/30 = x/ 360
5/30 * 360 = x
x = 60