A figure with an angle of rotation of $17^{\circ}$ has rotational symmetry of order 3.

  • True
  • False

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The correct option is B: False


The concept of rotational symmetry involves an object looking the same after a certain degree of rotation. The order of rotational symmetry refers to how many times an object matches up with its original shape during a full ($360^\circ$) rotation.

The formula to determine the order of rotational symmetry is: $$ \text{Order} = \frac{360}{x} $$ where $x$ is the angle of rotation in degrees.

For this specific problem: $$ \frac{360}{17} \approx 21.18 $$

Since $\frac{360}{17}$ is not a natural number, the object does not have a defined order of rotational symmetry with an angle of $17^\circ$. Therefore, the given statement is false.

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