Question

provide two different degrees of rotation less than 150° but greater than 0° that will turn a regular pentagon onto itself. (1 point) 144 156 45 72

Explanation:

Step1: Recall rotation formula for regular polygon

The formula to find the angle of rotation that maps a regular polygon onto itself is $\frac{360^{\circ}}{n}$, where $n$ is the number of sides of the polygon. For a pentagon, $n = 5$.

Step2: Calculate the basic angle of rotation

$\frac{360^{\circ}}{5}=72^{\circ}$. This is the smallest non - zero angle of rotation that maps a regular pentagon onto itself.

Step3: Find other valid angles

We can find other angles by multiplying the basic angle by positive integers. $2\times72^{\circ}=144^{\circ}$. Both $72^{\circ}$ and $144^{\circ}$ are between $0^{\circ}$ and $150^{\circ}$.

Answer:

$72$, $144$