Library / /144 of 213

, 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.

Want a route through all this instead of an archive? The track puts 2,444 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.