Question

The side QR of APQR is produced on both sides to points A and B as shown in the figure.
Prove that ZPQA + ZPRB - 180 = LQPR.

Answer 1

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

Given, Bisectors of ∠PQRand ∠PRS meet at point T.To prove: ∠QTR=

Given, Bisectors of ∠PQRand ∠PRS meet at point T.To prove: ∠QTR= 2

Given, Bisectors of ∠PQRand ∠PRS meet at point T.To prove: ∠QTR= 21

Given, Bisectors of ∠PQRand ∠PRS meet at point T.To prove: ∠QTR= 21

Given, Bisectors of ∠PQRand ∠PRS meet at point T.To prove: ∠QTR= 21 ∠QPR.

Given, Bisectors of ∠PQRand ∠PRS meet at point T.To prove: ∠QTR= 21 ∠QPR.Proof,

Given, Bisectors of ∠PQRand ∠PRS meet at point T.To prove: ∠QTR= 21 ∠QPR.Proof,∠TRS=∠TQR+∠QTR (Exterior angle of a triangle equals to the sum of the two interior angles.)

Given, Bisectors of ∠PQRand ∠PRS meet at point T.To prove: ∠QTR= 21 ∠QPR.Proof,∠TRS=∠TQR+∠QTR (Exterior angle of a triangle equals to the sum of the two interior angles.)⇒∠QTR=∠TRS−∠TQR --- (i)

Given, Bisectors of ∠PQRand ∠PRS meet at point T.To prove: ∠QTR= 21 ∠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

Given, Bisectors of ∠PQRand ∠PRS meet at point T.To prove: ∠QTR= 21 ∠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+∠PQR2∠TRS=∠QPR+2∠TQR

Given, Bisectors of ∠PQRand ∠PRS meet at point T.To prove: ∠QTR= 21 ∠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+∠PQR2∠TRS=∠QPR+2∠TQR∠QPR=2∠TRS−2∠TQR

Given, Bisectors of ∠PQRand ∠PRS meet at point T.To prove: ∠QTR= 21 ∠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+∠PQR2∠TRS=∠QPR+2∠TQR∠QPR=2∠TRS−2∠TQR ⇒ 2/1

1

1 ∠QPR=∠TRS−∠TQR (ii)