In Fig. 6.15, < PQR = 2 PRQ, then prove that <PQR = < PRT

1.	In Fig. 6.15, < PQR = 2 PRQ, then prove that <PQR = < PRT
Answer» Given, ∠PQR= ∠PRQ To prove:∠PQS= ∠PRT Proof: ∠PQR+∠PQS =180° (by LinearPair axiom) ∠PQS=180°– ∠PQR— (i) ∠PRQ+∠PRT= 180° (by Linear Pair axiom) ∠PRT= 180° – ∠PRQ ∠PRQ=180°– ∠PQR — (ii) [∠PQR = ∠PRQ] From (i) and (ii) ∠PQS= ∠PRT= 180°– ∠PQR ∠PQS= ∠PRT Hence, ∠PQS = ∠PRT

Answer»

Given,

∠PQR= ∠PRQ

To prove:∠PQS= ∠PRT

Proof:

∠PQR+∠PQS =180° (by LinearPair axiom)

∠PQS=180°– ∠PQR— (i)

∠PRQ+∠PRT= 180° (by Linear Pair axiom)

∠PRT= 180° – ∠PRQ

∠PRQ=180°– ∠PQR — (ii)

[∠PQR = ∠PRQ]

From (i) and (ii)

∠PQS= ∠PRT= 180°– ∠PQR

∠PQS= ∠PRT

Hence, ∠PQS = ∠PRT

Discussion