qr is produced to point S if d bisector of

in triangle PQR,

angle P+Q+R=180

So

P=180-(Q+R)....(i)

now

in triangle QRT,

 angle TQR=Q/2

angle QRT=QRP+PRT

=R+[(1/2) (PRS)]

=R+[(1/2)(180-R)]

=(R/2)+90

In triangle QTR,

 angle  QTR+QRT+TQR=180

So,

QTR=180-{[(R/2)+90+(Q/2)]}

=90-[(R+Q)/2]

=90-[(180-P)/2].....from (i)

=P/2

Hence proved.

=