linear pair

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.

linear pair