Question

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

Answer 1

Answer:

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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