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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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