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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