Chapter 9.3, Problem 13PPS

To determine

To find: The angle of rotation to the nearest tenth of a degree that maps P to $P^{\prime }$ .

Answer to Problem 13PPS

The angle of rotation to the nearest tenth of a degree that maps P to $P^{\prime }$ is $154.2°$ .

Explanation of Solution

Consider the figure shown below.

  

Figure (1)

The total angle made by the center of flower with seven petal is $360°$ .

The angle made by each petal is calculated as,

  $\begin{array}{c}{\text{Angle}}_{\text{Each}\text{Petal}}=\frac{360°}{7}\\ =51.4°\end{array}$

The angle made by $3$ petal is,

  $\begin{array}{c}{\text{Angle}}_{3\text{petals}}=51.4°\times 3\\ =154.2°\end{array}$

Therefore, the angle of rotation to the nearest tenth of a degree that maps P to $P^{\prime }$ is $154.2°$ .