Question

in triangle PQR,the angular Bisectors of angle Q and angle R of triangle PQR meet at point O. prove that angle QOR = 90°+1⁄2 angle P​

Answer 1

Answer:

Given that

OQ and  OR are angle bisector of Q and R

PQR is a triangle

also from  figure OQR is a triangle

Let angle Q= 2x

angle R = 2y

Now in ∆ PQR

angle Q +  angle R + angle P = 180°

or 2x + 2y +angle P = 180°

=> x +  y = 90° - 1/2 angle P .. . .  . . .. . (i)

Now in ∆OQR

angle RQO + angle QRO + angle O = 180

as angle RQO = x (from figure)

and angle QRO = y(from figure)

=> x + y + angle O = 180°

=> angle O = 180° - (x + y) . .. ..(ii)

Now from (i)and (ii)

Angle O = 180° - ( 90° - 1/2 angle P )

=> angle O = 90° + 1/2 angle P

hope this helped