Question

the bisectors of angle pqr and angle prs meet at o. prove that angle qtr =1/2 angle qpr . if angle qtr=40° find angle qpr​

Answer 1

Answer:

Given, Bisectors of ∠PQRand ∠PRS meet at point T.

To prove: ∠QTR=

2

1

∠QPR.

Proof,

∠TRS=∠TQR+∠QTR (Exterior angle of a triangle equals to the sum of the two interior angles.)

⇒∠QTR=∠TRS−∠TQR --- (i)

Also ∠SRP=∠QPR+∠PQR

2∠TRS=∠QPR+2∠TQR

∠QPR=2∠TRS−2∠TQR

⇒

2

1

∠QPR=∠TRS−∠TQR --- (ii)

Equating (i) and (ii),

∴∠QTR=

2

1

∠QPR [henceproved]