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. rotational symmetry? yes no angle? ° rotational symmetry? yes no angle? °

Explanation:

Step1: Analyze the first figure (rectangle)

A rectangle has rotational symmetry. The full rotation is \(360^{\circ}\). The number of times it coincides with itself in a full rotation: for a rectangle, it coincides with itself 2 times (at \(180^{\circ}\) and \(360^{\circ}\)). The formula for the smallest angle of rotation \(\theta=\frac{360^{\circ}}{n}\), where \(n\) is the number of times it coincides. Here \(n = 2\), so \(\theta=\frac{360^{\circ}}{2}=180^{\circ}\)

Step2: Analyze the second figure (three - armed shape)

This figure has rotational symmetry. The number of times it coincides with itself in a full rotation (\(360^{\circ}\)) is \(n = 3\). Using the formula \(\theta=\frac{360^{\circ}}{n}\), substituting \(n = 3\), we get \(\theta=\frac{360^{\circ}}{3}=120^{\circ}\)

Answer:

First figure: Rotational symmetry? Yes, Angle: \(180^{\circ}\)
Second figure: Rotational symmetry? Yes, Angle: \(120^{\circ}\)