Question

In the fig ,anglePQR=anglePRQ,Then prove that anglePQS=anglePRT​

Answer 1

Answer:

Step-by-step explanation:

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