Question

In the given fig LPQR=LPRQ , then prove that PQS=PRT.​

Answer 1

Step-by-step explanation:

In the given figure,

angle PQR=anglePRQ........(given)...(1)

Therefore, anglePQS=anglePQR.......(angles in linear pair)

Therefore, anglePRT=anglePRQ.....(angles in linear pair)

But, anglePQR=anglePRQ.....(from 1)

Therefore, anglePQS=anglePRT

Hence proved.

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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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