Question

pls solve ques. 6
plz plz plz
Tomorrow is my exam

Answer 1

In triangle PQR,
‹TRS=‹QTR+‹TQR[ext. ‹ property]
=1/2‹PRS=‹QTR+1/2‹PQR[QT & RT bisect‹Q & ‹PRS]
In triangle PQR,
‹PRS=‹QPR+‹PQR
=1/2‹PRS=1/2‹QPR+1/2‹PQR---(1)
=‹QTR+1/2‹PQR=1/2‹QPR+1/2‹PQR[using(1)]
=‹QTR=1/2‹QPR

BEST OF LUCK FOR YOUR EXAM.

Answer 2

Heya :))

Your answer:-

Since QT is bisector of angle PQR,
angle PQR = angle RQT----------(1)

since RT is the bisector of angle PRS,
angle PRT = angle TRS------------(2)

We know that exterior angle of a triangle is equal to sum of it's interior opposite angles.

In angle PQR,

ext. angle PRS = angle QPR + angle PQR

(angle PRT + angle TRS) = angle QPR + (angle PQT + angle RQT)

Angle TRS + angle TRS = angle QPR + (angle RQT + angle RQT). (using (1) and (2))

2 angle TRS = angle QPR + 2angle RQT

2(angle TRS - angle RQT) = angle QPR-----(3)

Now, in triangle QTR;
ext. angle TRS = angle QTR + angle ROT---(4) ( exterior angle of a triangle is equal to sum of its interior opposite angle)

Putting angle TRS in terms of angle QTR and angle RQT from (4) and (3), we get:

angle QTR + angle RQT - angle RQT = 1/2 angle QPR

Hence, angle QTR = 1/2 angle QPR

Hope it will helps u