Linear pair is a pair of adjacent angles (link) where non-common side forms a straight line

 

So, In a linear pair, there are two angles who have

  • Common vertex
  • Common side
  • Non-common side makes a straight line or Sum of angles is 180°

34.jpg

 

Linear pair

Linear pair is a pair of adjacent angles where non-common side forms a straight line

 

So, In a linear pair, there are two angles who have

  • Common vertex
  • Common side
  • Non-common side makes a straight line or Sum of angles is 180°

35.jpg

36.jpg

 

Here, these angles are in linear pair as

  • They have common vertex O.
  • They have common side OB
  • Non Common side (AC) is a straight line.

Here,

  ∠1 + ∠2 = 180°

Sum of linear pair = 180°   

 

Let’s take this figure

37.jpg

In this figure

  ∠1 & ∠2 are linear pair

   ∠2 & ∠3 are linear pair

  ∠3 & ∠4 are linear pair

  ∠4 & ∠1 are linear pair

 

38.jpg

So,

     ∠1 + ∠2 = 180°

     ∠2 + ∠3 = 180°

     ∠3 + ∠4 = 180°

     ∠4 + ∠1 = 180°

Let’s take some more examples.

 

Do the angles form a linear pair?

39.jpg

Here,

  Angles have a common vertex O,

  They have a common side OB

Now,

  Sum of angles = 40° + 140°

   = 180°

  ∴ Non-common sides from a line

 

Hence, angles form a linear pair.

 

Do the angles form a linear pair?

40.jpg

Here,

Angles have a common vertex O,

They have a common side OB

 

But,

Non-common side of ∠1 and ∠2

Do not form a line

 

∴  They do not form a linear pair

 

Do the angles form a linear pair?

41.jpg

 

Here,

Angles have a common vertex O,

They have a common side OQ

 

Now,

  Sum of angles = 60° + 90°

   = 150°

   ≠ 180°

  ∴ Non-common sides do not form a line

Hence, angle do not form a linear pair

 

Do the angles form a linear pair?

42.jpg

Here,

Angle do not have  common vertex

 

∴ They do not form a linear pair

 

Do the angles form a linear pair?

43.jpg

Here,

Angles have a common vertex O,

They have a common base OB

 

Now,

  Sum of angles = 65° + 115° = 180°

Since sum of angles is 180°

∴ They form a linear pair

  1. Chapter 5 Class 7 Lines and Angles
  2. Concept wise
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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.