Question

The hexagon GIKMPR and FJN are regular. The dashed line segments
form 30° angles.

Answer 1

K

Explanation:

Angle GOK measures 240° counterclockwise from G. GO≅KO, so G will map to K when it is rotated 240° CCW around point O.

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Comment on rotations with unspecified direction

Since positive angles in the coordinate plane are measured counterclockwise (from the +x axis), we presume that rotations through positive angles are rotations in the counterclockwise direction. If your textbook author has chosen a different convention, use that. (240° CW would map G to P.)