In triangle pqr oq and or are bisectors of angle q and angle r such that angle q is equal to angle r show that angle roq is equal to angle qro
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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
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