Question

in a figure side qr of pqr is produced to point s if bisectors of angle pqr and angle prs meets at point t then prove that angle qtr= half of angle qpr

Answer 1

let angles q be 2x as they are angle bisectors one part is X and other part is X so that they add up to 2x
similarly let angle PRS be 2y
we can write p+q=2y exterior angle property of triangle
also we can write t+x=y

now we have got 2eqations
p+2x=2y
t+X=y
on solving we get......
p=2{y-x}
=p/2=y-x
now t =y-x. so putting the value of y-x from previous eqn in t we get
t=p/2 proved

Answer 2

Hello mate ☺

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Solution:

∠PQT=∠TQR               (Given)

∠PRT=∠TRS               (Given)

To Prove:  ∠QTR=1/2(∠QPR)

∠PRS=∠QPR+∠PQR

(If a side of a triangle is produced, then the exterior angle is equal to the sum of two interior opposite angles.)

⇒∠QPR=∠PRS−∠PQR

⇒∠QPR=2∠TRS−2∠TQR

⇒∠QPR=2(∠TRS−∠TQR)

=2(∠TQR+∠QTR−∠TQR)                          (∠TRS=∠TQR+∠QTR)

(If a side of a triangle is produced, then the exterior angle is equal to the sum of two interior opposite angles.)

⇒∠QPR=2(∠QTR)

⇒∠QTR=1/2(∠QPR)

Hence Proved

I hope, this will help you.☺

Thank you______❤

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