Linear Pair Of Angles

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.
Linear-Pair-Of-Angles
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.
Linear-Pair-Of-Angle-theorem-1
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