Question

In a given figure, PQ is the diameter of the circle with center O, PR and QS are produced to meet at T and angle ROS is equal to 70°. Calculate the angle RTS.

• A. 15
• B. 17
• C. 19
• D. 13

Hint:

In circle geometry, always use the properties of the diameter and the relationships between angles formed by the intersection of secants and tangents.

Answer 1

The Correct Option is B

Step 1: Understand the geometry of the situation.
In the given problem, PQ is the diameter of the circle. According to the property of circles, the angle subtended by the diameter at the circumference is a right angle, meaning: \[ \angle PRQ = 90^\circ. \] Step 2: Use the angle given.
We are given that \( \angle ROS = 70^\circ \). Step 3: Calculate the angle RTS.
Since PR and QS are produced to meet at T, we observe that \( \angle ROS \) and \( \angle RTS \) are related. By the properties of angles in a cyclic quadrilateral and linear pairs, we have: \[ \angle RTS = 180^\circ - \angle ROS = 180^\circ - 70^\circ = 110^\circ. \] Step 4: Conclusion.
Therefore, the measure of angle RTS is \( \boxed{60^\circ} \). The correct answer is option (1).