Answer
425.4k+ views
Hint: We recall the definition of linear pair angles and vertically opposite angles in order to find them. We check linear pair angles first at each point of intersection of lines and note them. Later, we find the vertically opposite angles at each point of intersection of lines and note them.
Complete step-by-step answer:
We have a figure given that has three lines intersecting each other. We have 12 angles namely 1,2,3,….12. We need to find the angles that are linear pairs and vertically opposite angles.
Before that we recall what are linear pair angles and vertically opposite angles.
Linear pair angles are two angles that lie on the same line and the sum of those two angles are supplementary (sum of angles = $ {{180}^{o}} $ ).
Vertically opposite angles are two angles that are opposite to each other at the point where two lines intersect each other. Vertically opposite angles are always equal.
Let us first find the linear pair angles in the problem.
We can see that $ \angle 1 $ and $ \angle 4 $ lie on the same and the sum of those two angles is $ {{180}^{o}} $ . So, we can say $ \angle 1 $ and $ \angle 4 $ are linear pairs.
We can see that $ \angle 1 $ and $ \angle 2 $ lie on same and sum of those two angles is $ {{180}^{o}} $ . So, we can say $ \angle 1 $ and $ \angle 2 $ are linear pair.
We can see that $ \angle 2 $ and $ \angle 3 $ lie on same and sum of those two angles is $ {{180}^{o}} $ . So, we can say $ \angle 2 $ and $ \angle 3 $ are linear pair.
We can see that $ \angle 4 $ and $ \angle 3 $ lie on same and sum of those two angles is $ {{180}^{o}} $ . So, we can say $ \angle 4 $ and $ \angle 3 $ are linear pair.
We can see that $ \angle 5 $ and $ \angle 6 $ lie on same and sum of those two angles is $ {{180}^{o}} $ . So, we can say $ \angle 5 $ and $ \angle 6 $ are linear pair.
We can see that $ \angle 5 $ and $ \angle 8 $ lie on same and sum of those two angles is $ {{180}^{o}} $ . So, we can say $ \angle 5 $ and $ \angle 8 $ are linear pair.
We can see that $ \angle 6 $ and $ \angle 7 $ lie on same and sum of those two angles is $ {{180}^{o}} $ . So, we can say $ \angle 6 $ and $ \angle 7 $ are linear pair.
We can see that $ \angle 7 $ and $ \angle 8 $ lie on same and sum of those two angles is $ {{180}^{o}} $ . So, we can say $ \angle 7 $ and $ \angle 8 $ are linear pair.
We can see that $ \angle 9 $ and $ \angle 10 $ lie on same and sum of those two angles is $ {{180}^{o}} $ . So, we can say $ \angle 9 $ and $ \angle 10 $ are linear pair.
We can see that $ \angle 9 $ and $ \angle 12 $ lie on same and sum of those two angles is $ {{180}^{o}} $ . So, we can say $ \angle 9 $ and $ \angle 12 $ are linear pair.
We can see that $ \angle 10 $ and $ \angle 11 $ lie on same and sum of those two angles is $ {{180}^{o}} $ . So, we can say $ \angle 10 $ and $ \angle 11 $ are linear pair.
We can see that $ \angle 11 $ and $ \angle 12 $ lie on same and sum of those two angles is $ {{180}^{o}} $ . So, we can say $ \angle 11 $ and $ \angle 12 $ are linear pair.
Now, we find the vertically opposite angles.
We can see that $ \angle 1 $ and $ \angle 3 $ lie opposite to each other at the point of intersection of lines. So, we can say $ \angle 1 $ and $ \angle 3 $ are vertically opposite angles.
We can see that \[\angle 2\] and $ \angle 4 $ lie opposite to each other at the point of intersection of lines. So, we can say \[\angle 2\] and $ \angle 4 $ are vertically opposite angles.
We can see that \[\angle 5\] and \[\angle 7\] lie opposite to each other at the point of intersection of lines. So, we can say \[\angle 5\] and \[\angle 7\] are vertically opposite angles.
We can see that \[\angle 6\] and \[\angle 8\] lie opposite to each other at the point of intersection of lines. So, we can say \[\angle 6\] and n\[\angle 8\] are vertically opposite angles.
We can see that \[\angle 9\] and \[\angle 11\] lie opposite to each other at the point of intersection of lines. So, we can say \[\angle 9\] and \[\angle 11\] are vertically opposite angles.
We can see that \[\angle 10\] and \[\angle 12\] lie opposite to each other at the point of intersection of lines. So, we can say \[\angle 10\] and \[\angle 12\] are vertically opposite angles.
The linear pair angles are:
1) $ \angle 1 $ and $ \angle 4 $
2) $ \angle 1 $ and $ \angle 2 $
3) $ \angle 2 $ and $ \angle 3 $
4) $ \angle 4 $ and $ \angle 3 $
5) $ \angle 5 $ and $ \angle 6 $
6) $ \angle 5 $ and $ \angle 8 $
7) $ \angle 6 $ and $ \angle 7 $
8) $ \angle 7 $ and $ \angle 8 $
9) $ \angle 9 $ and $ \angle 10 $
10) $ \angle 9 $ and $ \angle 12 $
11) $ \angle 10 $ and $ \angle 11 $
12) $ \angle 11 $ and $ \angle 12 $
The vertically opposite angles are:
1) $ \angle 1 $ and $ \angle 3 $
2) \[\angle 2\] and $ \angle 4 $
3) \[\angle 5\] and \[\angle 7\]
4) \[\angle 6\] and \[\angle 8\]
5) \[\angle 9\] and \[\angle 11\]
6) \[\angle 10\] and \[\angle 12\]
Note: We should not confuse the definition of linear pair angles with vertically opposite angles. We always need to make sure that linear pair angles lie on a line sum is ${{180}^{o}}$. We also need to make sure that we find vertically opposite angles without any confusion.
Complete step-by-step answer:
We have a figure given that has three lines intersecting each other. We have 12 angles namely 1,2,3,….12. We need to find the angles that are linear pairs and vertically opposite angles.
Before that we recall what are linear pair angles and vertically opposite angles.
Linear pair angles are two angles that lie on the same line and the sum of those two angles are supplementary (sum of angles = $ {{180}^{o}} $ ).
Vertically opposite angles are two angles that are opposite to each other at the point where two lines intersect each other. Vertically opposite angles are always equal.
Let us first find the linear pair angles in the problem.
We can see that $ \angle 1 $ and $ \angle 4 $ lie on the same and the sum of those two angles is $ {{180}^{o}} $ . So, we can say $ \angle 1 $ and $ \angle 4 $ are linear pairs.
We can see that $ \angle 1 $ and $ \angle 2 $ lie on same and sum of those two angles is $ {{180}^{o}} $ . So, we can say $ \angle 1 $ and $ \angle 2 $ are linear pair.
We can see that $ \angle 2 $ and $ \angle 3 $ lie on same and sum of those two angles is $ {{180}^{o}} $ . So, we can say $ \angle 2 $ and $ \angle 3 $ are linear pair.
We can see that $ \angle 4 $ and $ \angle 3 $ lie on same and sum of those two angles is $ {{180}^{o}} $ . So, we can say $ \angle 4 $ and $ \angle 3 $ are linear pair.
We can see that $ \angle 5 $ and $ \angle 6 $ lie on same and sum of those two angles is $ {{180}^{o}} $ . So, we can say $ \angle 5 $ and $ \angle 6 $ are linear pair.
We can see that $ \angle 5 $ and $ \angle 8 $ lie on same and sum of those two angles is $ {{180}^{o}} $ . So, we can say $ \angle 5 $ and $ \angle 8 $ are linear pair.
We can see that $ \angle 6 $ and $ \angle 7 $ lie on same and sum of those two angles is $ {{180}^{o}} $ . So, we can say $ \angle 6 $ and $ \angle 7 $ are linear pair.
We can see that $ \angle 7 $ and $ \angle 8 $ lie on same and sum of those two angles is $ {{180}^{o}} $ . So, we can say $ \angle 7 $ and $ \angle 8 $ are linear pair.
We can see that $ \angle 9 $ and $ \angle 10 $ lie on same and sum of those two angles is $ {{180}^{o}} $ . So, we can say $ \angle 9 $ and $ \angle 10 $ are linear pair.
We can see that $ \angle 9 $ and $ \angle 12 $ lie on same and sum of those two angles is $ {{180}^{o}} $ . So, we can say $ \angle 9 $ and $ \angle 12 $ are linear pair.
We can see that $ \angle 10 $ and $ \angle 11 $ lie on same and sum of those two angles is $ {{180}^{o}} $ . So, we can say $ \angle 10 $ and $ \angle 11 $ are linear pair.
We can see that $ \angle 11 $ and $ \angle 12 $ lie on same and sum of those two angles is $ {{180}^{o}} $ . So, we can say $ \angle 11 $ and $ \angle 12 $ are linear pair.
Now, we find the vertically opposite angles.
We can see that $ \angle 1 $ and $ \angle 3 $ lie opposite to each other at the point of intersection of lines. So, we can say $ \angle 1 $ and $ \angle 3 $ are vertically opposite angles.
We can see that \[\angle 2\] and $ \angle 4 $ lie opposite to each other at the point of intersection of lines. So, we can say \[\angle 2\] and $ \angle 4 $ are vertically opposite angles.
We can see that \[\angle 5\] and \[\angle 7\] lie opposite to each other at the point of intersection of lines. So, we can say \[\angle 5\] and \[\angle 7\] are vertically opposite angles.
We can see that \[\angle 6\] and \[\angle 8\] lie opposite to each other at the point of intersection of lines. So, we can say \[\angle 6\] and n\[\angle 8\] are vertically opposite angles.
We can see that \[\angle 9\] and \[\angle 11\] lie opposite to each other at the point of intersection of lines. So, we can say \[\angle 9\] and \[\angle 11\] are vertically opposite angles.
We can see that \[\angle 10\] and \[\angle 12\] lie opposite to each other at the point of intersection of lines. So, we can say \[\angle 10\] and \[\angle 12\] are vertically opposite angles.
The linear pair angles are:
1) $ \angle 1 $ and $ \angle 4 $
2) $ \angle 1 $ and $ \angle 2 $
3) $ \angle 2 $ and $ \angle 3 $
4) $ \angle 4 $ and $ \angle 3 $
5) $ \angle 5 $ and $ \angle 6 $
6) $ \angle 5 $ and $ \angle 8 $
7) $ \angle 6 $ and $ \angle 7 $
8) $ \angle 7 $ and $ \angle 8 $
9) $ \angle 9 $ and $ \angle 10 $
10) $ \angle 9 $ and $ \angle 12 $
11) $ \angle 10 $ and $ \angle 11 $
12) $ \angle 11 $ and $ \angle 12 $
The vertically opposite angles are:
1) $ \angle 1 $ and $ \angle 3 $
2) \[\angle 2\] and $ \angle 4 $
3) \[\angle 5\] and \[\angle 7\]
4) \[\angle 6\] and \[\angle 8\]
5) \[\angle 9\] and \[\angle 11\]
6) \[\angle 10\] and \[\angle 12\]
Note: We should not confuse the definition of linear pair angles with vertically opposite angles. We always need to make sure that linear pair angles lie on a line sum is ${{180}^{o}}$. We also need to make sure that we find vertically opposite angles without any confusion.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)