Two lines ab and cd intersect each other at a point o such that zaoc: zaod=5:7. find all the angles.

AOC=DOB and AOD=COB5x+7x+5x+7x =360°24x=360°x=360°/24x=155x=75°

7x=105°

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Question 4 Lines And Angles Exercise 7B

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Answer:

Consider ∠AOC as 5x and ∠AOD as 7x

From the figure we know that ∠AOC and ∠AOD for linear pair of angles

So it can be written as

∠AOC + ∠AOD = 180

By substituting the values

5x + 7x = 180

On further calculation

12x = 180

By division

x = 180/12

x = 15

By substituting the value of x

∠AOC = 5x

So we get

∠AOC = 5 (15) = 75

∠AOD = 7x

So we get

∠AOD = 7 (15) = 105

From the figure we know that ∠AOC and ∠BOD are vertical angles

So we get

∠AOC = ∠BOD = 75

From the figure we know that ∠AOD and ∠BOC are vertical angles

So we get

∠AOD = ∠BOC = 105

Video transcript

"hello students welcome to leader learning question answer video solutions my name is biljot kaur and today's mathematics problem is two lines a b and c d intersects each other at point o such that aoc is to aod is 5 is to 7 now we have to figure out all the angles now see guys aoc is given as 5 since it's in the ratio so it's technically 5x similarly this is 7x now if you look at this thing this thing forms a straight line see guys this is a straight line that means we can use the identity of straight that states that x plus y will give us 180 degree so 5x plus 7x will give 180 or you can say 12x is equals to 180 or x is equals to 15. now since we have the value as x is equals to 15 so if i put this value into 5x so i will get the value as 75 similarly if i put this value in 7x so i will get 105. so that means if i remove this i can clearly say state that [Music] aoc is 75 degree [Music] and this is 105 degree now since we know that vertically opposite angles are equal so angle a o c is equals to angle b o d and angle c o b is equals to a o d that means this is also 75 degree and this is also 105 degree because vertically opposite angles are equal vertically opposite angles are equal thank you so much for watching the video kids if you have any questions any queries please drop down in the comment section for more fun videos subscribe to leo have a wonderful day"

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Text Solution

Answer : `angleAOC=75^(@)=angleBOD, angleAOD=105^(@)=angleBOC`

Solution : Let `AOC=(5x)^(@)` and `angleAOD=(7x)^(@)`. <br> `angleAOC+angleAOD=180^(@) implies 5x+7x=180 implies 12x=180 implies x=15`. <br> `:. angleAOC=(5xx15)^(@)=75^(@) and angleAOD=(7xx15)^(@)=105^(@)`. <br> `angleBOD=angleAOC=75^(@)` [vertically opposite `angles`] <br> `angleBOC=angleAOD=105^(@)` [vertically opposite `angles`].

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