The problem you've uploaded is asking to find the angle $x$ in a circle, applying the properties of regular polygons.

Observations:

1. The figure shows a circle with a chord and the corresponding arc.
2. $\angle x$ is inscribed in the circle.
3. The options for $x$ are:
   • A) 63°
   • B) 60°
   • C) 75°
   • D) 45°
   • E) 50°

Steps to Solve:

1. Inscribed Angle Theorem: The angle subtended by an arc at the center of a circle is twice the angle subtended at any point on the circumference by the same arc.

2. Identify the Relevant Angles: From the diagram:

   • $\angle C_1$ is likely the angle subtended at the center by the arc.
   • $\angle x$ is the inscribed angle.

3. Relation between $\angle C_1$ and $\angle x$:

   • If $\angle C_1$ is the central angle, then $\angle x = \frac{1}{2} \times \angle C_1$.

Conclusion:

Without additional specific values or details in the diagram, let's assume that the circle shown is a part of a regular polygon, likely implying symmetrical angles and equal division by the chords. Based on the given options and common angles in regular polygons, the angle $x$ is most likely 60° (since regular polygons like equilateral triangles lead to such inscribed angles).

Thus, Option B: 60° seems to be the correct answer.

Would you like more details on this topic, or do you have any further questions?

Related Questions:

1. What is the inscribed angle theorem, and how is it derived?
2. How do you calculate angles in a regular polygon?
3. How does the number of sides in a regular polygon affect the angle measures?
4. What is the relationship between central angles and inscribed angles?
5. How can you find angles in polygons that are not regular?

Tip:

When dealing with inscribed angles, always remember that they are half the measure of the central angle subtending the same arc. This property is crucial for solving many circle-related problems.