Question

In Fig. 6.15, ∠ PQR = ∠ PRQ, then prove that∠ PQS = ∠ PRT.

Answer 1

Answer:

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

Answer 2

Answer:

Since ST is a straight line so,

∠PQS+∠PQR = 180° (linear pair) and

∠PRT+∠PRQ = 180° (linear pair)

Now, ∠PQS + ∠PQR = ∠PRT+∠PRQ = 180°

Since ∠PQR =∠PRQ (as given in the question)

∠PQS = ∠PRT. (Hence proved).

Step-by-step explanation: