Question

angle PQR = angle PRQ, the prove that angle PQS= angle PRT​

Answer 1

Step-by-step explanation:

Given that,  ∠PQR=∠PRQ

from above figure, we have, 

∠PQS=180−∠PQR   

∠PRT=180−∠PRQ

∠PRT=180−∠PQR

∴∠PQS=∠PRT

Answer 2

Question :-

In figure, ∠PQR = ∠PRQ, then prove that ∠PQS = ∠PRT.

Answer :-

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

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