We want to determine the angles of rotational symmetry for the given polygon. To do so, let's draw segments from the vertices of the regular pentagon to the middle.
Notice that if we draw a circle in the middle of the pentagon we obtain five congruent angles.
Since a circle is 360^(∘), we know that the measure of each angle is equal to 72^(∘).
360^(∘)/5= 72^(∘)
Then, if we rotate the pentagon by 72^(∘), it will map onto itself.
The same is true if we rotate the image 144^(∘). Therefore, the correct options are D and G, respectively.
