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CEMC Gauss (Grade 8), 2023

Geometry Difficulty 2.4 Junior Find the answer Canada

In the diagram, $PQR$ is a
line segment, $\angle PQS = 125\degree$ , $\angle QSR=x\degree$ , and $SQ=SR$ .

What is the value of $x$ ?

Pick one

Solution

Of the 100 small identical squares, 28 are presently unshaded,
and so $100-28=72$ are shaded.

So that 75% of the area of $WXYZ$ is
shaded, 75 of the 100 small squares must be shaded.

Therefore, $75-72=3$ more of the
small squares must be shaded.

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