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 (right - angled triangle)

A right - angled triangle has no rotational symmetry. When rotated by any angle less than \(360^{\circ}\), it will not look the same as the original figure.

Step2: Analyze the second figure (equilateral triangle)

For an equilateral triangle, the formula for the angle of rotational symmetry is \(\frac{360^{\circ}}{n}\), where \(n\) is the number of sides. Since \(n = 3\) (equilateral triangle has 3 sides), the angle of rotation is \(\frac{360^{\circ}}{3}=120^{\circ}\).

Answer:

First figure: Rotational symmetry? No.
Second figure: Rotational symmetry? Yes, Angle? \(120^{\circ}\)