Question

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

Answer 1

It is given that O is the centre and  \[\angle ROS = 40° \]

We have `angle RQS = 1/2 angle ROS = 20°`

In right angled triangle RQT we have

\[\angle RQT + \angle QTR + \angle TRQ = 180° \]
\[ \Rightarrow 20° + \angle QTR + 90° = 180° \]
\[ \Rightarrow \angle QTR = 70° \]

\[\text{ Hence } , \angle RTS = 70° \]