Question

quadrilateral ( y e u v ) can be mapped onto quadrilateral ( d p l c ) by a rotation. if ( mathrm{m} angle y=150^{circ} ), find ( mathrm{m} angle d ).
answer
( mathrm{m} angle d ) can be determined. ( mathrm{m} angle d=square^{circ} ).

Explanation:

Step1: Recall Rotation Property

Rotation is a rigid transformation, which means it preserves the shape and size of the figure. So, corresponding angles of the two quadrilaterals (pre - image and image) are congruent.

Step2: Identify Corresponding Angles

Since quadrilateral \(YEUV\) is mapped onto quadrilateral \(DPLC\) by a rotation, \(\angle Y\) and \(\angle D\) are corresponding angles.

Step3: Determine the Measure of \(\angle D\)

Because corresponding angles in a rigid transformation (rotation) are congruent, \(m\angle D=m\angle Y\). Given that \(m\angle Y = 150^{\circ}\), then \(m\angle D=150^{\circ}\).

Answer:

\(150\)