Question

what is the minimum angle of rotational symmetry for the quadrilateral shown below? 60° 90° 180° 360°

Explanation:

Step1: Recall the concept of rotational symmetry

Rotational symmetry of a figure is the property that the figure looks the same after a rotation by a certain angle. The minimum angle of rotational symmetry is the smallest non - zero angle for which this is true.

Step2: Analyze the given quadrilateral

The given quadrilateral is a parallelogram. For a parallelogram, if we rotate it by \(180^{\circ}\), it maps onto itself. Rotating by \(60^{\circ}\) or \(90^{\circ}\) will not map a general parallelogram onto itself (since the sides and angles of a general parallelogram do not have the required congruence for these smaller angles). Rotating by \(360^{\circ}\) is a full rotation (trivial, as any figure maps onto itself after a \(360^{\circ}\) rotation), and \(180^{\circ}\) is the non - trivial minimum for a parallelogram.

Answer:

\(180^{\circ}\) (the third option)