In the given figure- line AB and CD intersect at O- If - COB - x - - BOD -4 x - and - AOD - y - then y -A- 12-B- 18-C- 40-D- 36-

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Vertically Opposite Angles

In the given ...

Question

In the given figure, line AB and CD intersect at O. If $∠ C O B = x^{\circ}$ , $∠ B O D = 4 x^{\circ}$ and $∠ A O D = y^{\circ}$ , then y= ______ .

12^{\circ}

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40^{\circ}

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18^{\circ}

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36^{\circ}

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Solution

The correct option is D $36^{\circ}$
Consider the straight line COD. Since the angles on a straight line equal 180 $^{\circ}$ , we have
$∠ C O B + ∠ B O D = 180^{\circ}$

$x^{\circ} + 4 x^{\circ} = 180^{\circ}$

$5 x^{\circ} = 180^{\circ}$

$x = 36^{\circ}$

Now, note that $∠ A O D = ∠ C O B$ (vertically opposite angles)

$∴ y = x = 36^{\circ}$

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Similar questions

Q. In the given figure, straight lines AB and CD intersect at O. If ∠AOC + ∠BOD = 130°, then ∠AOD = ?
(a) 65°
(b) 115°
(c) 110°
(d) 125°

In the figure below, lines AB and CD intersect each other at point O. Angles ( $∠$ AOD, $∠$ COB) and ( $∠$ AOC, $∠$ BOD) are called ___.

Q. In the figure, lines

A B

and

C D

intersect at

O

. If

∠ A O D : ∠ D O B = 4 : 5,

then

∠ C O B

is :

In the figure below, lines AB and CD intersect each other at point O. The angle pairs ( $∠ A O D$ and $∠ C O B$ ) and ( $∠ A O C$ and $∠ B O D$ ) are called ___.

Q. Two lines AB and CD intersect at O. If ∠AOC + ∠COB + ∠BOD = 270°, then ∠AOC =

(a) 70°

(b) 80°

(c) 90°

(d) 180°

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In the given figure, line AB and CD intersect at O. If ∠COB=x∘, ∠BOD=4x∘ and ∠AOD=y∘, then y= ______ .

The correct option is D 36∘Consider the straight line COD. Since the angles on a straight line equal 180∘, we have ∠COB+∠BOD=180∘ x∘+4x∘=180∘ 5x∘=180∘ x=36∘ Now, note that ∠AOD=∠COB (vertically opposite angles) ∴y=x=36∘

In the given figure, line AB and CD intersect at O. If $∠ C O B = x^{\circ}$ , $∠ B O D = 4 x^{\circ}$ and $∠ A O D = y^{\circ}$ , then y= ______ .