181k views
3 votes
What angles of rotation up to 360 that will carry a regular hexagon onto itself?

A. 30 degree counterclockwise rotation
B. 90 degree counterclockwise rotation
C. 120 degree counterclockwise rotation
D. 270 degree counterclockwise rotation

1 Answer

4 votes

Final answer:

A 120-degree counterclockwise rotation is the correct answer as it is a multiple of the 60° angle that represents the sixfold symmetry of a hexagon, carrying it onto itself.

Step-by-step explanation:

The angles of rotation that will carry a regular hexagon onto itself are 60°, 120°, 180°, 240°, 300°, and 360°. Among the given options, only a rotation of 120 degrees counterclockwise will carry a hexagon onto itself. This is because a regular hexagon has six sides and therefore sixfold symmetry; each side represents a fraction of the 360° full rotation, which is 360°/6 = 60°. Therefore, any multiple of this angle will map the hexagon onto itself. Option C, a 120 degree counterclockwise rotation, is such a multiple (2 × 60°) and is correct.

User Jorge Alfaro
by
8.6k points