In the figure, if $l_{1} | | l_{2}$ and $l_{3} | | l_{4}$ what is y in terms of x ?

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Solution

In the figure,

$l_{1} | | l_{2}$ and $l_{3} | | l_{4}$ and m is the angle bisector
$∴ ∠ 2 = ∠ 3 = y$
$∵ l_{1} | | l_{2}$
$∴ ∠ 1 = x$ (Corresponding angles)
$∵ l_{3} | | l_{4}$
$∴ ∠ 1 + (∠ 2 + ∠ 3) = 180^{0}$
(Co-interior angles)
$\Rightarrow x + 2 y = 180^{0}$
$\Rightarrow 2 y = 180^{0} - x$
$\Rightarrow y = \frac{180^{0} - x}{2} = 90^{0} - \frac{x}{2}$

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In the figure, if l1||l2 and l3||l4 what is y in terms of x ?

In the figure, l1||l2 and l3||l4 and m is the angle bisector ∴∠2=∠3=y ∵l1||l2 ∴∠1=x (Corresponding angles) ∵l3||l4 ∴∠1+(∠2+∠3)=1800 (Co-interior angles) ⇒x+2y=1800 ⇒2y=1800−x ⇒y=1800−x2=900−x2

In the figure, if $l_{1} | | l_{2}$ and $l_{3} | | l_{4}$ what is y in terms of x ?