Question

quadrilateral ( a ^ { prime } b ^ { prime } c ^ { prime } d ^ { prime } ) is the image of quadrilateral ( a b c d ) under a rotation about point ( q ). determine the angle of rotation.

Explanation:

Step1: Recall the property of rotation

When a figure is rotated about a point, the angle between a point and its image with respect to the center of rotation is the angle of rotation.

Step2: Analyze the rotation

Connect \(QA\) and \(QA'\). Since rotation is a rigid transformation, we can observe that the angle between \(QA\) and \(QA'\) is \(180^{\circ}\) (by the straight - line property and the position of the pre - image and image points around point \(Q\)).

Answer:

\(180^{\circ}\)