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Problem 206

Geometry Difficulty 1.3 Multiple choice CEMC Gauss (Grade 7) · Canada · 2014

A clockwise rotation around point $Z$ (that is, a rotation in the direction of the arrow) transforms the shaded quadrilateral to the unshaded quadrilateral.

The angle of rotation is approximately

Pick one

Official solution

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 $PZQ$ .

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 $270\degree$ .

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.