Question

Ben,cindy and tom cut a single cake into three slices.the sizes of the slices are proportional to their ages .

ben is 10 years old
cindy is 15 years old
Tom is 20 years old
What is the central angle of cindys slice?

Answer 1

120 degrees

Step-by-step explanation:
if the slices are proportional to their ages, they would each get some amount equal to whatever number this can be divided in. (ben is 10, he gets two slices, cindy gets three slices, tom gets four)

so nine slices total. there are 360 degrees in a circle. divide this by nine. since there are nine slices divided according to their ages (think of each slice as a 5 since all of their ages are multiples of five) and cindy is 15 years old, so she would get three slices of five to equal 15. she gets 3/9 of the cake.

divide 360/9 to get the central angle measure of JUST ONE slice, which would be 40 degrees. if you multiply this by three, you get 120 degrees.

hope this helped! :)

Answer 2

The central angle of Cindy's slice is 120 degrees.

Step-by-step explanation:

To find the central angle of Cindy's slice, we need to determine the proportion of her age to the total age of all three people. The total age is 10 + 15 + 20 = 45 years. Cindy's proportion is 15/45 = 1/3. To find the central angle, we multiply this proportion by 360 degrees, which is the total angle for a full circle. So, Cindy's slice has a central angle of (1/3) * 360 = 120 degrees.