Rotate segment AE about point F 144 degrees

DC

Step-by-step explanation:

If we rotate a segment around a point 360 degrees, we have rotated it around to its original point. Similarly, if we rotate it 180 degrees, we have rotated it to the side opposite of where it once was relative to the point.

What we can do is see how much 144 degrees is of 360 and use that to determine how far around we rotate AE around F.

144/360

divide by 12 because that is a common factor of both the numerator and denominator

12 / 30

divide by 2 because that is a common factor

6/15

divide by 3 because that is a common factor

2/5

Therefore, 144/360 = 2/5. This means that we rotate segment AE 2/5 of the way around point F. We have 5 sides in the polygon ABCDE, and each represents 1/5 of the way around. Going counterclockwise, ED represents 1/5, DC represents 2/5, and so on. We are looking for 2/5, so DC is our answer