Chapter 14.8, Problem 26WE

To determine

To state other rational symmetries of a figure which has $60°$ rotational symmetry.

Answer to Problem 26WE

The figure has $120°,180°,240°,300°\text{and360}°$ rotational symmetries in addition to $60°$ rotational symmetry.

Explanation of Solution

Given information:

The figurehas $60°$ rotational symmetry.

The figure has $120°,180°,240°,300°\text{and360}°$ rotational symmetries in addition to $60°$ rotational symmetry. If you rotate the figure $60°$ from its initial position it maps itself then again rotate it $60°$ it maps itself again because it has $60°$ rotational symmetry. Here the total rotation is $120°$ but the figure maps itself. Hence, if you rotate this object to an angle multiple of $60°$ the figure will map itself.