1. The problem asks for a degree of rotational symmetry of a regular pentagon. 2. A regular pentagon has 5 equal sides and 5 equal angles. 3. The formula for the degree of rotational symmetry of a regular polygon with $n$ sides is: $$\text{Degree of rotational symmetry} = \frac{360^\circ}{n}$$ 4. For a pentagon, $n=5$, so: $$\frac{360^\circ}{5} = 72^\circ$$ 5. This means the pentagon maps onto itself every $72^\circ$ rotation. 6. The question asks for a degree of rotational symmetry, which can be any multiple of $72^\circ$ less than $360^\circ$. 7. The multiples are $72^\circ$, $144^\circ$, $216^\circ$, and $288^\circ$. 8. Among the answer options, only $144^\circ$ matches one of these multiples. 9. Therefore, the correct answer is E. $144^\circ$.