In this geometric diagram, we are working with a circle and multiple angles formed by points on the circumference and a tangent line. We are asked to find the angle $x$, which is the angle formed between the tangent line $ST$ and the chord $RS$.

Key observations:

• $\triangle RQS$ is an inscribed triangle.
• $\angle QRS = 70^\circ$, and this is an interior angle of the triangle.
• $\angle PSO = 30^\circ$ is also provided.

Applying the Tangent-Chord Theorem:

The tangent-chord theorem states that the angle between a tangent and a chord is equal to the angle in the alternate segment of the circle.

In this case:

• The angle $x$ (between the tangent $ST$ and the chord $RS$) is equal to the angle $\angle QRS$, which is $70^\circ$.

Thus, $x = 70^\circ$.

Would you like further clarification or details on this? Here are 5 related questions to deepen your understanding:

1. How does the tangent-chord theorem work in other configurations?
2. What are the properties of angles in cyclic quadrilaterals?
3. Can the angle sum properties in circles help in finding missing angles?
4. What other theorems are useful in solving circle-related problems?
5. How can you identify when to apply the tangent-segment theorem?

Tip: Always look for cyclic quadrilaterals and tangents in circle problems—they often unlock solutions via symmetry and special angle theorems.