If the bisectors of ∠ PQR and ∠ PRS meet at point T, then prove that ∠ QTR = 1/2 ∠QPR.

NCERT CLASS 9 CHAPTER 6 Exercise 6.3 Lines and Angels Question No. 6

Page No. 6

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∠PRS is the exterior angle of △PQR.

Therefore,

∠PRS = ∠QPR + ∠PQR

⇒ 1/2 ∠PRS = 1/2 ∠QPR + 1/2 ∠PQR

⇒ ∠TRS = 1/2 ∠QPR + ∠TQR …(1)[∵ ∠TRS = 1/2 ∠PRS and ∠TQR = 1/2 ∠PQR]

∠TRS is exterior angle of △TQR

Therefore,

∠TRS = ∠QTR + ∠TQR …(2)

From, the equations (1) and (2), we have

∠QTR + ∠TQR = 1/2 ∠QPR + ∠TQR

⇒ ∠QTR = 1/2 ∠QPR