Rotation is the process of turning a given object about a point to produce its replica. So that the angle of rotation required in the question is [tex]120^{o}[/tex].
Rotational symmetry is a process that requires the rotation of a given object about a reference point to produce its image which has the same or exact characteristics. This implies that its dimensions, measure of internal angles and size do not change except its orientation. The orientation implies how the object is positioned.
The sum of an angle formed at a point is [tex]360^{o}[/tex]. Thus turning a given object about a point implies its rotation with respect to a measured or given angle.
Thus in the diagram given in the question, the pattern shown divides the angle at the centered point into three equal parts.
i.e [tex]\frac{360^{o} }{3}[/tex] = [tex]120^{o}[/tex]
Therefore, rotating the figure about its center at an angle of [tex]120^{o}[/tex] would produce an image with the same characteristics as the figure.
So, it can be concluded that the angle of rotation required in the question is [tex]120^{o}[/tex] i.e option B.
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