Question

in the given figure , the side QR of triangle PQR is produced to a point S. if the bisectors of angle PQR and angle PRS meet at point T, then prove that angle QTR is equal to half of angle QPR​ ( answer fast in easy method )

Answer 1

Answer:

Step-by-step explanation:

1) consider angle Q as 2x hence angle PQT and angle TQR are respectively x so altogether they sum up to 2x and let angle TRS and angle TRP to be y which will sum up to be 2y { angle R) .

2) In triangle TQR , angle TQR + angle QTR + angle TRS ( Exterior angle property )

which equates as - {x + angle QTR  = y}

so angle QTR = {y - x}                  - (1)

3) In Triangle PQR , {angle QPR + angle PQR = angle PRS}

so angle QPR + 2x = 2y

angle QPR/2 = y - x          ( dividing each side by 2 )    - (2)

4) From -(1) and (2) we get

Angle QTR =Angle QPR/2