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$x$ and $y$ are complementary angles such that $x : y = 1 : 2$. Express the given information as a system of linear equations in two variables and hence solve it.
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$x + y = 90^{\circ}$
$2x = y$
Solving to get $x = 30^{\circ}, y = 60^{\circ}$
$2x = y$
Solving to get $x = 30^{\circ}, y = 60^{\circ}$