Question

the figure below has rotational symmetry. is the smallest possible rotation that results in the figure being mapped onto itself.

Explanation:

Step1: Understand Rotational Symmetry

Rotational symmetry means a figure can be rotated by an angle and coincide with its original position. The smallest such angle is the order's related angle. For a figure with rotational symmetry, we check angles like \(90^\circ\), \(180^\circ\), \(360^\circ\) etc.

Step2: Analyze the "H" - shaped Figure

The given figure (like an "H"): when rotated by \(180^\circ\) around its center, it maps onto itself. Rotating by \(90^\circ\) won't (the top and side parts won't align). So the smallest rotation angle for this figure to map onto itself is \(180^\circ\).

Answer:

\(180^\circ\)