A.68
Linear pair of angles:
If Non common arms of two adjacent angles form a line, then these angles are called linear pair of angles.
Axiom- 1
If a ray stands on a line, then the sum of two adjacent angles so formed is 180°i.e, the sum of the linear pair is 180°.
Axiom-2
If the sum of two adjacent angles is 180° then the two non common arms of the angles form a line.
The two axioms given above together are called the linear pair axioms.
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Solution:
Given,
∠PQR = ∠PRQ
To prove:
∠PQS = ∠PRT
Proof:
∠PQR +∠PQS =180° (by Linear Pair axiom)
∠PQS =180°– ∠PQR — (i)
∠PRQ +∠PRT = 180° (by Linear Pair axiom)
∠PRT = 180° – ∠PRQ
∠PRQ=180°– ∠PQR — (ii)
[∠PQR = ∠PRQ]
From (i) and (ii)
∠PQS = ∠PRT = 180°– ∠PQR
∠PQS = ∠PRT
Hence, ∠PQS = ∠PRT
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