Question

Answer this question and score marks!!​

Answer 1

It is a question of chapter 6 class 9 ncert book right.

ST is a straight line.

∴ ∠PQR + ∠PQS = 180° …(1) [Linear pair]

Similarly, ∠PRT + ∠PRQ = 180° …(2) [Linear Pair]

From (1) and (2), we have

∠PQS + ∠PQR = ∠PRT + ∠PRQ

But ∠PQR = ∠PRQ [Given]

∴ ∠PQS = ∠PRT

Answer 2

Answer:

Given angle(PQR) = angle(PRS)

proof:- angle (PQS) = angle ( PRT )

Solution :-

by using exterior angle property

angle(PQS) = angle( PRQ)+ angle( RPQ).

so we can write this

angle(PQS) - angle(RPQ). = angle( PRQ). (i)

now ,

angle(PRT) = angle(PQR) + angle(QPR)

we can write this also,

angle(PRT) - angle(QPR) = angle(PQR). (ii)

according to question

angle(PQR) = angel(PRQ)

so, we can equate both (i) and (ii) equations

and we get

after equation both the equation angle(QPR) and angle(RPQ) get cancel and we get

angle (PQS) = angle (PRT)

hence proved.

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