Library / CEMC Gauss (Grade 8) /277 of 525

CEMC Gauss (Grade 8), 2014

Algebra Difficulty 1.3 Junior Find the answer Canada

Consider the set of fractions $\left\{\frac37,\:\frac32,\:\frac67,\:\frac35\right\}$ . Ordered from smallest to largest, the set is

Pick one

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 $270\degree$ .

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

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