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

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1. Chapter 5 Class 7 Lines and Angles
2. Concept wise
3. Adjacent Angles, Linear Pair of angles, Vertically Opposite angles

Adjacent Angles, Linear Pair of angles, Vertically Opposite angles 