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Step-by-step explanation:
To proove : <ROP + <TOQ = 90 degrees
Angle PSO + angle SOQ = 180 degrees ( Linear pair )
Now it is given that OR and OS are angle bisectors.
Hence,
ANGLE ROP = ROS =X. ------1
and angle SOT = TOQ =Y. ------2
hence
2X + 2Y = 180 degrees
X + Y = 90 degrees
which implies angle POR + QOT = 90. (FROM 1 AND 2)
Hence proved
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