Question

3. In Fig. 6.15, Z PQR = 2 PRQ, then prove that
Z PQS = Z PRT.

Answer 1

Answer:

∠PQS = ∠PRT

Step-by-step explanation:

ST is a straight line and sum of angle in linear pair always equal to 180

∠PQS + ∠PQR = 180° … (1)

And

∠PRT + ∠PRQ = 180° … (2)

From equation (1) and (2).we get:

∠PQS + ∠PQR = ∠PRT + ∠PRQ … (3)

But given that ∠PQR = ∠PRQ

Plug the value we get

∠PQS + ∠PRQ =∠PRT + ∠PRQ

∠PQS = ∠PRT + ∠PRQ - ∠PRQ

∠PQS = ∠PRT

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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