Q. 93.7( 4 Votes )

In Fig. 16.138, O is the centre of a circle and PQ is a diameter. If ROS=40°, find RTS.

Answer :

Since,

PQ is diameter


Then,


PRQ = 90o (Angle in semi-circle)


Therefore,


PRQ + TRQ = 180o (Linear pair)


90o + TRQ = 180o


TRQ = 90o


By degree measure theorem,


ROS = 2 RQS


RQS = 20o


In triangle RQT, we have


RQT + QRT + RTS = 180o (By angle sum property)


20o + 90o + RTS = 180o


RTS = 70o


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