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, 2021

Geometry Difficulty 2.5 Junior Find the answer Canada

In the diagram, $PQR$ is a straight line segment.

If $x + y = 76$ , what is the value of $x$ ?

Pick one

Solution

Since $PQR$ forms a straight angle, then $x^\circ + y^\circ + x^\circ + y^\circ + x^\circ = 180^\circ$ which gives $3x + 2y = 180$ .

Since $x+y=76$ and $2x+2y+x = 180$ , then $2(76) + x = 180$ or $x = 180 - 152 = 28$ .

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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.