Question

side QR of triangle pqr is produced to a point S as shown in the figure the bisector of a meets q r s t prove that angle pqr + angle PRS equals to 2 PTR​

Answer 1

««triangle PQR IS equilatral triangle so each angle will be 60°

therefore

angle PRQ + angle PRS =180°

BECAUSE QRS is a straight line

therefore

angle PQR+angle PRS=180°

[because angle PQR=angle PRQ which is in equiangular triangle]»»LHS

««Here PT is perpendicular to QR which is 90°

there 2*angle PTR=2*90°=180°»»RHS

Therefore angle PQS+ angle PRS= 2 * angle PTR

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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