Vertically Opposite angles

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,

  ∠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 

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

Now,

∠3 & ∠1 are vertically opposite angles

  ∴ ∠3 = ∠1

    ∠3 = 30° 

Also,  ∠2 & ∠4 are vertically opposite angles

   ∴ ∠2 = ∠4      ......(1)                             

Now,

  ∠1 & ∠2 are linear pair

               ∴ ∠1 + ∠2 = 180°

    30° + ∠2 = 180°

    ∠2 = 180° − 30°     

  ∠2 = 150°

From (1)

∠4 = ∠2

∠4 = 150°

So, our figure looks like