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Based on the given image, we have a cyclic quadrilateral \( PQRS \) inscribed in a circle, with angles provided as follows:
- \( \angle RQS = 70^\circ \)
- \( \angle PSQ = 30^\circ \)
- There is an external angle \( x \) formed by extending line segment \( PS \) to point \( T \).

### Steps to Find the Value of \( x \):

1. **Use the Exterior Angle Theorem**:
   The exterior angle of a cyclic quadrilateral is equal to the opposite interior angle. Therefore, we have:
   \[
   x = \angle RQS = 70^\circ
   \]

Hence, the value of \( x \) is \( 70^\circ \).

Would you like more details on the concept of cyclic quadrilaterals or any other clarifications?

### Follow-Up Questions
1. What are the properties of a cyclic quadrilateral that make this calculation possible?
2. How does the sum of opposite angles in a cyclic quadrilateral relate to its geometry?
3. Can you provide another example where the Exterior Angle Theorem applies in cyclic quadrilaterals?
4. What happens to the angles of the quadrilateral if it is not cyclic?
5. How can we prove that a quadrilateral is cyclic using its angles?

### Tip:
Remember, in a cyclic quadrilateral, the sum of the opposite angles is always \( 180^\circ \). This property is crucial for solving many circle-related geometry problems.

Given a cyclic quadrilateral PQRS inscribed in a circle, where ∠RQS = 70° and ∠PSQ = 30°, and line PS is extended to point T forming an external angle x. What is the value of x?

Learn how to find the external angle x formed by extending a side of a cyclic quadrilateral PQRS inscribed in a circle. Using the Exterior Angle Theorem, we calculate that x = 70°. This problem covers key concepts of cyclic quadrilaterals and circle geometry. Suitable for students in Grades 9-11.

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