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.
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