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The problem shows a circle with a central point \( O \). There are points \( U \), \( S \), and \( P \) on the circumference, and the angle \( \angle USP = 35^\circ \) is inscribed in the circle. The goal is to find the angle \( x \), which is \( \angle UOP \), the central angle subtended by the arc \( UP \).

### Solution:
In a circle, the central angle is twice the inscribed angle that subtends the same arc. This is a known property of circles.

Given:
- Inscribed angle \( \angle USP = 35^\circ \)

We need to find:
- Central angle \( x = \angle UOP \)

Using the property:
\[
x = 2 \times \angle USP = 2 \times 35^\circ = 70^\circ
\]

### Answer:
The value of \( x \) is \( 70^\circ \).

Would you like further details or have any questions?

### Follow-up Questions:
1. What is the relationship between a central angle and an inscribed angle subtended by the same arc in a circle?
2. How would you find the length of the arc subtended by a central angle?
3. Can an inscribed angle be larger than its corresponding central angle?
4. How would the result change if \( \angle USP \) were given as \( 40^\circ \)?
5. What is the formula for finding the area of a sector based on the central angle?

**Tip:** Always remember that the central angle of a circle is twice the inscribed angle that subtends the same arc.

Find the value of x, where x is the central angle subtended by an arc in a circle. Given that the inscribed angle subtending the same arc is 35°.

Learn how to find the central angle in a circle when given the inscribed angle subtending the same arc. This problem utilizes the central angle theorem and is suitable for students in Grades 8-10.

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