The spinner at right is designed so that if you randomly spin the spinner and land in the shaded sector, you win $\$1{,}000{,}000$. Unfortunately, if you land in the unshaded sector, you win nothing. Assume point $C$ is the center of the spinner.  

1. If $m∠ACB=90°$, how many times would you have to spin to reasonably expect to land in the shaded sector? How did you get your answer?

   Hint (a):

   What fraction of the circle is the shaded region? How can this help you?

   Answer (a):

   $4 \; \text{times}$

2. What if $m∠ACB=1°$? How many times would you have to spin to reasonably expect to land in the shaded sector?

   Hint (b):

   Use the same method you used for part (a).

3. Suppose $P \left(\text{winning} \; \$1{,}000{,}000\right) = \frac{1}{5}$ for each spin. What must $m∠ACB$ equal? Show how you got your answer.

   Hint (c):

   If this is the reverse of the method used for part (a), what must you do?

   Answer (c):

   $\frac{360°}{5}=72°$