Question
In figure, rays $AB$ and $CD$ intersect at $O$. Determine $x$ when $y = 40^\circ .$
✓
Answer
Here, $\angle\text{AOC}+\angle\text{BOC}=180^\circ$ [linear pair]
$\Rightarrow 2x + y = 180^\circ $
$\Rightarrow 2x + 40 = 180^\circ $
$\Rightarrow 2x = 180 - 40 = 140^\circ $
$\Rightarrow 2x = 140^\circ $
$\Rightarrow x = 70^\circ $
$\Rightarrow 2x + y = 180^\circ $
$\Rightarrow 2x + 40 = 180^\circ $
$\Rightarrow 2x = 180 - 40 = 140^\circ $
$\Rightarrow 2x = 140^\circ $
$\Rightarrow x = 70^\circ $
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