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Question Can we have a figure with rotational symmetry whose smallest angle of symmetry is
(a) 45 °?
(b) 17°?
(a) Since, the complete rotation is 360°. Then, if the given angle divides 360°, it can be an angle of symmetry.
Here, \(\frac{360^{\circ}}{45^{\circ}}\) = 8, which is a whole number.
Therefore, 45° can be the smallest angle of symmetry of a figure.
(b) Here, \(\frac{360^{\circ}}{17^{\circ}}\) = 21 \(\frac{3}{17}\), which is not a whole number.
Therefore, 17° cannot be the smallest angle of symmetry.