Chapter 3, Problem 66E

Angeline and Brad are planning to divide the chocolate-strawberry cake shown in Fig 3-40(a) using the divider-chooser method, with Angelina being the divider. Suppose that Angelina values chocolate cake three times as much as she values strawberry cake. Fig 3-40(a) shows a generic cut made by Angelina dividing the cake into two shares $s_1$ and $s_2$ of equal value to her. Think of $s_1$ as an $"x"$ chocolate- $y°$ strawberry” share. For each given measure of the angel $x,$ find the corresponding measure of the angle of $y$.

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a. $x=60°$.

b. $x=72°$.

c. $x=108°$.

d. $x=120°$.