Question

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.

Explanation:

Step1: Recall the concept of rotational symmetry

A figure has rotational symmetry if it can be rotated by an angle less than \(360^{\circ}\) and still look the same. The formula for the smallest angle of rotation \(\theta=\frac{360^{\circ}}{n}\), where \(n\) is the number of congruent parts or the order of rotational symmetry.

Step2: Analyze the first figure (octagon - 8 - sided figure)

For a regular octagon (\(n = 8\)), using the formula \(\theta=\frac{360^{\circ}}{8}\).

$$ \theta = 45^{\circ} $$

Step3: Analyze the second figure (arrow)

The arrow does not have rotational symmetry. If we rotate it by any angle less than \(360^{\circ}\), its orientation changes.

Answer:

• First figure: Rotational symmetry? Yes, Angle: \(45^{\circ}\)
• Second figure: Rotational symmetry? No, Angle: (not applicable)