Question

q. 1 . In the given figure angle PQR = PRQ then prove that angle PQS = angle PRT

please give me answer ...​

Answer 1

Given: ∠PQR = ∠PRQ

To Prove: ∠PQS = ∠PRT

Here,

• ∠PQR + ∠PQS = 180° (Linear Pair)

➯ ∠PQS = 180° - ∠PQR

➯ ∠PQS = 180° - ∠PRQ ...(Equation X)

[∵ ∠PQR = ∠PRQ (Given)]

• ∠PRQ + ∠PRT = 180° (Linear Pair)

➯ ∠PRT = 180° - ∠PRQ ...(Equation Y)

∴ Equation X = Equation Y, i.e.

∠PQS = ∠PRT. ...Hence, Proved.

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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