Question

in given figure angle pqr = angle prs proive that angle pqs is equal to angle prt​

Answer 1

Answer:

<PQS + <PQR = 180 (Linear Pair)

=)<PQS = 180 - <PQR (i)

<PRT + <PRQ = 180 (Linear Pair)

=)<PRQ = 180 - <PRQ (ii)

NOW:-

<PQR = <PRQ (Given)

180 - <PQR = 180 - <PRQ

=)<PQS = <PRQ

Hence Proved

Hope it helped

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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