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In the diagram PQR is a triangle where the bisectors of interior angle ∠PQR and exterior angle ∠PRT intersect at a point S. If ∠QSR = 45°, then what is the value of ∠QPR ?

In the diagram PQR is a triangle where the bisectors of interior angle ∠PQR and exterior angle ∠PRT intersect at a point S. If ∠QSR = 45°, then what is the value of ∠QPR ? Correct Answer 90°

Given:

⇒ 2y = 2x + ∠QPR

⇒ ∠QPR = 2y – 2x = 2 × (y – x)      ----(1)

Again similarly,

∠SRT = ∠RQS + ∠RSQ

⇒ y = x + 45°

⇒ y – x = 45°     ----(2)

Using (2) in (1), we get,

∠QPR = 2 × 45° = 90°

∴ the value of ∠QPR is 90°

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