Question

In the figure given above, $PQ$ is a diameter of the circle whose centre is at O. If $\angle ROS={44}^{\circ }$, then what is the value of $\angle RTS$?

• A. ${46}^{\circ }$
• B. ${64}^{\circ }$
• C. ${69}^{\circ }$
• D. None of the above

Answer 1

The correct option is D None of the above

Arc $RS$ subtends ${44}^{\circ }$ at the centre O; so it subtends half the angle at $Q$ i.e., $\angle RQT={22}^{\circ }$.
$\angle PRQ={90}^{\circ }$
$\therefore \angle TRQ={90}^{\circ }$
Hence, $\angle RTS={90}^{\circ }-{22}^{\circ }={68}^{\circ }$