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  $$\mathrm{\angle }ROS=40°$$

We have ${\displaystyle \angle RQS=\frac{1}{2}\angle ROS=20°}$

In right angled triangle RQT we have

$$\mathrm{\angle }RQT+\mathrm{\angle }QTR+\mathrm{\angle }TRQ=180°$$
$$\Rightarrow 20°+\mathrm{\angle }QTR+90°=180°$$
$$\Rightarrow \mathrm{\angle }QTR=70°$$

$$\text{ Hence },\mathrm{\angle }RTS=70°$$