Problem 196

The measure of $\angle PZQ$ formed by the bottom edge of the shaded quadrilateral, $ZQ$, and this same edge after the rotation, $ZP$, is approximately $90\degree$. The transformation of the shaded quadrilateral to the unshaded quadrilateral is a clockwise rotation around point $Z$ through an angle equal to the measure of reflex angle $PZQ$. [[IMAGE0]] The measure of $\angle PZQ$ added to the measure of reflex $\angle PZQ$ is equal to the measure of one complete rotation, or $360\degree$. Therefore, the measure of reflex angle $PZQ$ is approximately $360\degree-90\degree$ or $270\degree$. Thus the clockwise rotation around point $Z$ is through an angle of approximately $270\degree$.