CAT Linear Pair of Angles - Practice Questions & MCQ

Linear Pair of Angle: Two adjacent angles form a linear pair of angles if their non-common arms are two opposite rays, i.e., the sum of two adjacent angles is 180°.

In the above figure, ∠AOC and ∠BOC form a linear pair of angles.

Axiom 1: If a ray stands on a line, then the sum of two adjacent angles so formed is 180°. 

Let's see, how this is possible.

We have given A ray CD stands on a line AB such that ∠ACD and ∠BCD are formed. (As said in axiom). Now draw CE perpendicular to AB.

Axiom 2 (Converse of Axiom 1): If the sum of two adjacent angles is 180°, then the non-common arms of the angles form a line.

In the axiom above, it is giiven that, two adjacent angles ∠AOC and ∠BOC with common arm OC such that ∠AOC + ∠BOC = 180°. So we need to see if OA and OB are in the same straight line, i.e., AOB is a straight line.

Let's assume that, AOB is not a straight line. Then, produce AO to D so that AOD is a straight line. 

By our assumption, AOD is a straight line and ray OC lies on it.

For obvious reasons, the two axioms above together is called the Linear Pair Axiom.