Question

on the class
In the given figure angle PQR= PRQ, then prove that ?
PQS = PRT.

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Answer 1

Given:

∠PQR = ∠PRQ

To Prove:

∠PQS = ∠PRT

Solution:

Let ∠PQR = x

hence:

∠PRQ = x ⠀(given ∠PQR = ∠PRQ)

Now:

∠PQS + ∠PQR = 180° (linear pair)

⟹ ∠PQS = 180° - ∠PQR

⟹ ∠PQS = 180° - x⠀.....( 1 )

also we can say that,

∠PRT + ∠PRQ = 180° (linear pair)

⟹ ∠PRT = 180° - ∠PRQ

⟹ ∠PRT = 180° - x⠀......( 2 )

From ( 1 ) and ( 2 )

∠PQS = ∠PRT

${\boxed{\sf{\red{hence\:proved}}}}$