To find the value of $x$ in this circle diagram, we can apply properties of inscribed angles and central angles. Here’s a step-by-step solution:

1. Understanding the Inscribed and Central Angles Relationship:

   • The angle $\angle BOC$ (denoted as $x$) is a central angle.
   • The angle $\angle BAC$ (30°) is an inscribed angle that subtends the same arc $BC$ as the central angle $\angle BOC$.

2. Applying the Inscribed Angle Theorem:

   • The Inscribed Angle Theorem states that an inscribed angle is half the measure of the central angle subtending the same arc.
   • Therefore, we can set up the equation: $x = 2 \times 30^\circ$

3. Solving for $x$: $x = 60^\circ$

Thus, the value of $x$ is $60^\circ$.

Would you like additional details, or do you have any questions on this?

Here are some related questions that might deepen your understanding:

1. What is the Inscribed Angle Theorem, and how is it derived?
2. How does the Inscribed Angle Theorem apply to different types of polygons inscribed in circles?
3. Can this method be used to find unknown angles in all circular configurations?
4. How does this theorem relate to the concept of arc length?
5. What other theorems in geometry are essential when working with circles?

Tip: When solving for angles in a circle, always check for relationships between inscribed and central angles as they can simplify the problem significantly.