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Standard VI

Mathematics

Intersecting and Parallel Lines

In the given ...

Question

In the given figure, two lines $A B$ and $C D$ intersect at $O$ . Ray $O E$ is perpendicular to the line $A B$ . If $a : b = 3 : 7,$ then find reflex $∠ B O D$ .

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Solution

In the given figure,

We have,

$a : b = 3 : 7$

$∠ E O A = 90^{o}$

Let $a = 3 x, b = 7 x$

Since,
$∠ E O C + ∠ B O C + ∠ E O A = 180^{o}$

$3 x + 7 x + 90^{o} = 180^{o}$

$x = 9^{o}$

Thus $a = 27^{o}$ and $b = 63^{o}$

Now,

$= ∠ A O B + ∠ B O D$

$= 63^{o} + ∠ B O D = 180^{o}$

$= ∠ B O D = 117^{o}$

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In the given figure, two lines AB and CD intersect at O. Ray OE is perpendicular to the line AB. If a:b=3:7, then find reflex ∠BOD.

In the given figure,We have,a:b=3:7∠EOA=90oLet a=3x,b=7xSince,∠EOC+∠BOC+∠EOA=180o3x+7x+90o=180ox=9oThus a=27o and b=63oNow,=∠AOB+∠BOD=63o+∠BOD=180o=∠BOD=117o

In the given figure, two lines $A B$ and $C D$ intersect at $O$ . Ray $O E$ is perpendicular to the line $A B$ . If $a : b = 3 : 7,$ then find reflex $∠ B O D$ .