The problem involves a circle with a central angle and two inscribed angles. Let’s break this down step by step to find the value of $x$.

1. Key Concept: The measure of an inscribed angle is half the measure of the central angle that subtends the same arc.

   • In this case, the central angle is given as $150^\circ$.
   • The two inscribed angles (marked as $x$) are subtending the same arc as the central angle.

2. Relation between central and inscribed angle: $x = \frac{1}{2} \times 150^\circ$ $x = 75^\circ$

Final Answer:

$x = 75^\circ$

Would you like further explanation or additional examples?

Here are 5 related questions to explore further:

1. What is the general formula for the relationship between central and inscribed angles?
2. How does the inscribed angle theorem apply to other parts of a circle?
3. If the central angle was changed to $120^\circ$, what would be the new value of $x$?
4. What happens if multiple inscribed angles share the same arc? Do they all have the same value?
5. How do central angles compare when measured in radians instead of degrees?

Tip: Always remember that an inscribed angle is half the central angle when both subtend the same arc. This is a crucial property for solving problems involving circles!