When two lines intersect,

  angles opposite to each other vertically opposite angles.

 

Vertically opposite angles have

  • Common vertex
  • And are opposite to each other

Here,

44.jpg

  ∠1 & ∠2 have common vertex O

  & are opposite to each others

So, they are vertically opposite angles.

 

Also,

  Vertically opposite angles are equal

  ∴ ∠1 = ∠2 

 

Let’s take this figure 

45.jpg

Here,

  ∠1 & ∠3 are vertically opposite angles

  ∴ ∠1 = ∠3 

  ∠2 & ∠4 are vertically opposite angles

  ∴ ∠2 = ∠4 

Let’s do some questions

 

Find ∠ 2, ∠3, ∠4

46.jpg

Now,

∠3 & ∠1 are vertically opposite angles

  ∴ ∠3 = ∠1

    ∠3 = 30° 

Also,  ∠2 & ∠4 are vertically opposite angles

   ∴ ∠3 = ∠1      ......(1)                             

47.jpg

Now,

  ∠1 & ∠2 are linear pair

               ∴ ∠1 + ∠2 = 180°

    30° + ∠2 = 180°

    ∠2 = 180° − 30°     

  ∠2 = 150°

48.jpg

From (1)

∠4 = ∠2

∠4 = 150°

So, our figure looks like

        

  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.