2008 Grade 8 CEMC Gauss Problems/Problem 3

Problem

In the diagram, $\angle PQR = 90^{\circ}$ .

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The value of $x$ is

$\text{ (A) }\ 30 \qquad\text{ (B) }\ 60 \qquad\text{ (C) }\ 90 \qquad\text{ (D) }\ 10 \qquad\text{ (E) }\ 45$

Solution

From the diagram, we can see that $m\angle PQS = 2x^{\circ}$ , $m\angle RQS = x^{\circ}$ , and $m\angle PQS + m\angle RQS = m\angle PQR = 90^{\circ}$ .

This allows us to solve for $x$ :

$2x + x = 90$

$3x = 90$

$x = \boxed {\textbf {(A) } 30}$

~anabel.disher

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2008 Grade 8 CEMC Gauss Problems/Problem 3

Problem

Solution