**Linear Pair Of Angles**

Two adjacent angles are said to form a linear pair of angles, if their non-common arms are two opposite rays.

In the adjoining figure, ∠AOC and ∠BOC are two adjacent angles whose non-common arms OA and OB are two opposite rays, i.e., BOA is a line

∴ ∠AOC and ∠BOC form a** linear pair of angles**.

**Theorem 1:**

Prove that the sum of all the angles formed on the same side of a line at a given point on the line is 180°.

**Given:** AOB is a straight line and rays OC, OD and OE stand on it, forming ∠AOC, ∠COD, ∠DOE and ∠EOB.

**To prove:** ∠AOC + ∠COD + ∠DOE + ∠EOB = 180°.

**Proof:** Ray OC stands on line AB.

∴ ∠AOC + ∠COB = 180°

⇒ ∠AOC + (∠COD + ∠DOE + ∠EOB) = 180°

[∵ ∠COB = ∠COD + ∠DOE + ∠EOB]

⇒ ∠AOC + ∠COD + ∠DOE + ∠EOB = 180°.

Hence, the sum of all the angles formed on the same side of line AB at a point O on it is 180°.

**Theorem 2:**

Prove that the sum of all the angles around a point is 360°.

**Given:** A point O and the rays OA, OB, OC, OD and OE mak