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Standard XII

Mathematics

Condition for Two Lines to Be Parallel

In the adjoin...

Question

In the adjoining figure line p $| |$ line q. Line t and line s are transversals. Find measure of $∠$ x and $∠$ y using the measures of angles given in the figure.

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Solution

$40^{\circ} + u = 180^{\circ} \Rightarrow u = 140^{\circ} ω + u = 180^{\circ} \Rightarrow ω = 180 ° - u = 40 ° ∠ z = 70 °$ (vertically opposite angles)
$∠ y + ∠ z = 180 °$
$\Rightarrow ∠ y = 180 ° - ∠ z 180 ° - 70 ° = 110 °$
$\Rightarrow ω + x = 180^{\circ}$
$∴ x = 140^{\circ}$

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In the adjoining figure line p $| |$ line q. Line t and line s are transversals. Find measure of $∠$ x and $∠$ y using the measures of angles given in the figure.

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In the adjoining figure line p|| line q. Line t and line s are transversals. Find measure of ∠x and ∠y using the measures of angles given in the figure.

40∘+u=180∘⇒u=140∘ω+u=180∘⇒ω=180°−u=40°∠z=70°(vertically opposite angles)∠y+∠z=180°⇒∠y=180°−∠z180°−70°=110°⇒ω+x=180∘∴x=140∘

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In the adjoining figure line p $| |$ line q. Line t and line s are transversals. Find measure of $∠$ x and $∠$ y using the measures of angles given in the figure.