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This problem involves a circle with intersecting lines, and we need to find the value of angle \( x \).

### Step-by-step solution:
1. **Identify the key angles:**
   - There is an inscribed angle of \( 35^\circ \), adjacent to the angle \( x \).
   - An external angle \( 141^\circ \) is also given.

2. **Recall the relationship between an exterior angle and the intercepted arc:**
   The exterior angle theorem states that the exterior angle of a circle is equal to half the difference of the intercepted arcs.

   Specifically:
   \[
   \text{Exterior Angle} = \frac{1}{2}(\text{Larger Intercepted Arc} - \text{Smaller Intercepted Arc})
   \]
   In this case, the angle \( x \) is the exterior angle to the arc, so:
   \[
   x = \frac{1}{2}(141^\circ - 35^\circ)
   \]

3. **Calculate \( x \):**
   \[
   x = \frac{1}{2}(141^\circ - 35^\circ) = \frac{1}{2} \times 106^\circ = 53^\circ
   \]

So, the value of \( x \) is **53 degrees**.

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Would you like further clarification or details? Here are some related questions to expand on this:

1. What is the exterior angle theorem and how does it apply to circles?
2. How do we calculate the sum of opposite angles in a cyclic quadrilateral?
3. What are inscribed and central angles in a circle, and how do they relate?
4. How do intercepted arcs affect the calculation of angles in a circle?
5. Can the exterior angle of a triangle be applied similarly in circle problems?

**Tip:** When solving circle geometry problems, look for relationships between angles, arcs, and lines, as these often help simplify complex configurations.

Find the value of x in a circle where an inscribed angle is 35° and an external angle is 141°.

Learn how to solve a circle geometry problem involving inscribed and external angles. In this case, we are asked to find the value of x when given a 35° inscribed angle and a 141° external angle. This problem uses the exterior angle theorem and explores key circle geometry concepts.

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