Track / Stage 2 / 56 of 240 #296 of 2444

Problem 296

Combinatorics Difficulty 2.4 Multiple choice CEMC Gauss (Grade 8) · Canada · 2022

A public holiday is always celebrated on the third Wednesday of a
certain month. In that month, the holiday cannot occur on which of the
following days?

Pick one

Official solution

$\triangle PQR$ is isosceles
with $PQ=PR$ , and so $\angle PRQ=\angle PQR$ .

The sum of the angles in $\$\triangle$
PQR $is$ $180\degree\$.$

Since $\angle QPR=70\degree$ , then
the other two angles in this triangle add to $180\degree-70\degree=110\degree$ .

Since these two angles are equal, they each measure $110\degree \div 2= 55\degree$ , and so
$x=55$ .

Since $QRST$ is a rectangle, each of
its interior angles is a right angle, and so $y=90$ .

The value of $x+y$ is $55+90=145$ .

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