Question

angle pqr is equal to angle prq then prove that angle pqr is equal to up prt

Answer 1

Solutions:

Since rays QP and RP stand on ST.

Hence, ∠SQP + ∠PQR = 180° and ∠SRP + ∠PRT = 180°

=> ∠PQS + ∠PQR = 180° and ∠PRQ + ∠PRT = 180°

=> ∠PQS + ∠PQR = ∠PRQ + ∠PRT

=> ∠PQS + ∠PQR = ∠PQR + ∠PRT ________[Since, ∠PRQ = ∠PQR (Given)]

=> ∠PQS = ∠PRT

( Refer to the attachment )

Answer 2

Firstly, Refer to the attachment.

• Given : ∠PQR = ∠PRT

• To Prove : ∠PQS = ∠PRT

• Proof :

On Line ST,

∠PQR + ∠PQS = 180° --- ( Linear Pair )

Taking ∠PQS to the other side,

∠PQR = 180° - ∠PQS ----- ( 1 )

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∠PRQ + ∠PRT = 180° --- ( Linear Pair )

Taking ∠PRT to the other side,∠PRQ = 180° - ∠PRT ---- ( 2 )

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Now, it's given that ∠PQR = ∠PRQ

And we know that ∠PQR = 180° - ∠PQS -- ( From 1 )

We also know that ∠PRQ = 180° - ∠PRT -- ( From 2 )

Substituting these, we get :

180° - ∠PQS = 180° - ∠PRT

Taking the 180° on left hand side to the other side, we get :

- ∠PQS = 180° - ∠PRT - 180°

Both 180° will get cancelled.

Now we have,

- ∠PQS = - ∠PRT

When we cancel both the minus signs, we're left with :

∠PQS = ∠PRT

Hence Proved!