for each figure below, determine if it has rotational symmetry. if it does, give the smallest angle of…

for each figure below, determine if it has rotational symmetry. if it does, give the smallest angle of rotation needed for the figure to appear unmoved. rotational symmetry? yes no angle? ° rotational symmetry? yes no angle? °

for each figure below, determine if it has rotational symmetry. if it does, give the smallest angle of rotation needed for the figure to appear unmoved. rotational symmetry? yes no angle? ° rotational symmetry? yes no angle? °

Answer

Explanation:

Step1: Analyze the 'X' figure

A figure has rotational symmetry if it can be rotated about a point and still look the same. For the 'X' figure, it can be rotated. The 'X' has 2 - fold rotational symmetry. The full - turn is 360°. To find the smallest angle of rotation, we divide 360° by the order of rotational symmetry. Since the order of rotational symmetry of 'X' is 2, the smallest angle of rotation $\theta=\frac{360^{\circ}}{2}=180^{\circ}$.

Step2: Analyze the 'F' figure

The letter 'F' does not look the same after any rotation less than 360°. So it has no rotational symmetry.

Answer:

For the 'X' figure: Rotational symmetry? Yes Angle? 180° For the 'F' figure: Rotational symmetry? No Angle? N/A