Question

in figure lines ab and cd intersect each other at point o.if angle aoc : angle boc =5:7 find all the angles​

Answer 1

Answer:

angle AOC = angle BOD =75

angle BOC = angle AOD = 105

Step-by-step explanation:

measure of angle is x

angle AOC = 5x

angle AOD = 7x

hence,

ang AOC + ang AOD = 180.....linear pair

5x + 7x = 180

12x=180

x= 180

x= 180 / 12 = 15

hence, angle AOC = angle BOD.......opposite angles

angle AOC = angle BOD = 5x = 5 x 15 = 75

similarly,

angle BOC = angle AOD .opposite angles

angle BOC = angle AOD = 7x = 7 x 15

= 105

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Answer 2

$\huge \rightarrowtail \tt \: ANSWER \: \leftarrowtail$

Given :-

Lines AB and CD intersect each other at a point O .

∠AOC : ∠BOC = 5 : 7

Required to find :-

• Measures of all the angles

Concept used :-

• Vertically opposite angles are equal

• Sum of a linear pair is supplementary

Solution :-

We can solve this question in 2 methods !

1st method :-

Given :-

∠AOC : ∠BOC = 5 : 7

So,

Let,

∠AOC = 5x°

∠BOC = 7x°

( Refer to the attachment )

From the diagram we can conclude that ;

∠AOC and ∠BOC form an linear pair

So,

∠AOC + ∠BOC = 180°

[Reason :- Sum of a linear pair is supplementary ]

Hence,

5x° + 7x° = 180°

12x° = 180°

x° = 180°/12

x° = 15°

So,

∠AOC = 5x = 5 ( 15 )° = 75°

∠BOC = 7x = 7 ( 15 )° = 105°

Now,

We can conclude that ;

∠AOC = ∠BOD

∠ BOC = ∠AOD

[ Reason :- Vertically Opposite angles are equal ]

Hence,

This implies ,

∠BOD = 75°

∠AOD = 105°

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2nd method :-

Consider the given ratio ;

That is ,

∠AOC : ∠BOC = 5 : 7

So,

Let,

∠AOC = 5x°

∠BOC = 7x°

Now,

Refer to the attachment ,

From the given diagram we can conclude that ;

∠AOC = ∠BOD

∠BOC = ∠AOD

[ Reason : Vertically Opposite angles ]

This implies ,

∠BOD = 5x°

∠AOD = 7x°

However,

We can also conclude that ,

∠AOC + ∠BOC + ∠AOD + ∠BOD = 360°

[ Reason :- They form a complete angle ]

So,

5x° + 7x° + 7x° + 5x° = 360°

24x° = 360°

x° = 360°/24

x° = 15°

Hence,

∠AOC = 5x° = 5 ( 15 )° = 75°

∠BOC = 7x° = 7 ( 15 )° = 105°

This implies

=> ∠BOD = 75°

=> ∠AOD = 105°

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