Three lines AB- CD- and EF interesect each other at O-If - AOE - 30- and - DOB - 40- find - COF-

From the given figure, we have ∠ AOE + ∠ EOD + ∠ DOB = 180^∘ nbsp;[∴Sum of all angles on a straight line is 180^∘] ⇒ 30^∘ + ∠ EOD + 40^∘ ...

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Standard VI

Mathematics

Finding Unknown Angles

Three lines A...

Question

Three lines AB, CD, and EF interesect each other at O.
If $∠ A O E = 30^{\circ} a n d ∠ D O B = 40^{\circ}$ , find $∠ C O F .$

$70^{\circ}$

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$110^{\circ}$

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$55^{\circ}$

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$90^{\circ}$

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Solution

The correct option is B
$110^{\circ}$

From the given figure, we have
$∠ A O E + ∠ E O D + ∠ D O B = 180^{\circ} [∴ S u m o f a l l a n g l e s o n a s t r a i g h t l i n e i s 180^{\circ}] \Rightarrow 30^{\circ} + ∠ E O D + 40^{\circ} = 180^{\circ} \Rightarrow ∠ E O D = 180^{\circ} - 70^{\circ} \Rightarrow ∠ E O D = 110^{\circ}$
Again, $∠ E O D = ∠ C O F [v e r t i c a l l y o p p o s i t e a n g l e s] \Rightarrow ∠ C O F = 110^{\circ}$

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Question 94

Three lines AB, CD and EF interesect each other at O. If $∠ A O E = 30^{\circ} a n d ∠ D O B = 40^{\circ}$ (see the figure). Find $∠ C O F .$

In the given figure, three lines AB, CD and EF intersect at a point O such that $∠ A O E = 35^{\circ}$ and $∠ B O D = 40^{\circ}$ . Find the measure of $∠ A O C, ∠ B O F, ∠ C O F$ and $∠ D O E$ .

In the figure, lines AB and CD intersect each other at O.

If ∠AOC + ∠BOE = 70^o and ∠BOD = 40^o, find ∠BOE

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Three lines AB, CD, and EF interesect each other at O. If ∠AOE=30∘ and ∠DOB=40∘, find ∠COF.

The correct option is B 110∘ From the given figure, we have ∠AOE+∠EOD+∠DOB=180∘ [∴Sum of all angles on a straight line is 180∘]⇒30∘+∠EOD+40∘=180∘⇒∠EOD=180∘−70∘⇒∠EOD=110∘ Again, ∠EOD=∠COF [vertically opposite angles]⇒∠COF=110∘

Three lines AB, CD, and EF interesect each other at O.
If $∠ A O E = 30^{\circ} a n d ∠ D O B = 40^{\circ}$ , find $∠ C O F .$