Question

figure pqrs is rotated to form figure wxyz. which angle of figure wxyz corresponds with ∠r? ∠w ∠x ∠y ∠z

Explanation:

Step1: Understand rotation property

Rotation is a rigid transformation. Rigid transformations preserve the shape and size of the figure. So, corresponding angles of the original figure \(PQRS\) and the rotated figure \(WXYZ\) are equal.

Step2: Match the vertices

When a figure is rotated, the order of vertices is preserved. In figure \(PQRS\), the order of vertices is \(P - Q - R - S\). In figure \(WXYZ\), the order of vertices is \(W - X - Y - Z\). By comparing the order and the structure of the two - quadrilaterals (since rotation is a rigid motion and the relative position of vertices is maintained in terms of adjacency), we can see that vertex \(R\) in \(PQRS\) corresponds to vertex \(X\) in \(WXYZ\) in terms of the right - angle (by observing the orientation and the structure of the two figures, as the sides adjacent to the right - angle in \(PQRS\) (one horizontal and one vertical) have a corresponding pair of sides (one horizontal and one vertical) in \(WXYZ\) at vertex \(X\)).

Answer:

\(\angle X\)