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In the diagram, we see a circle with a center point \( C \), a central angle marked as \( 108^\circ \), and two inscribed angles labeled \( m \) and \( n \). The goal is likely to find the values of these angles \( m \) and \( n \).

### Key geometric principles:
1. **Inscribed Angle Theorem**: An inscribed angle is half of the central angle subtended by the same arc.
2. **Sum of angles around a point**: The angles formed at a point (such as at the center of a circle) sum to \( 360^\circ \).

#### Steps:
1. The central angle given is \( 108^\circ \). This means that the arc subtended by this central angle is the same arc subtended by both inscribed angles \( m \) and \( n \).
   
2. By the **Inscribed Angle Theorem**, each inscribed angle \( m \) and \( n \) is half of the central angle that subtends the same arc. Thus, the measures of \( m \) and \( n \) are:
   \[
   m = n = \frac{108^\circ}{2} = 54^\circ
   \]

So, both angles \( m \) and \( n \) are \( 54^\circ \).

Would you like further explanation or have any questions?

Here are some related questions:
1. What is the relationship between central and inscribed angles in a circle?
2. How do you determine the measure of an inscribed angle from the central angle?
3. Can two different inscribed angles subtend the same arc in a circle?
4. What is the sum of all central angles around a point inside a circle?
5. How can the Inscribed Angle Theorem be applied to other shapes or arcs?

**Tip**: Always remember that the central angle is twice any inscribed angle subtended by the same arc.

Find the values of the inscribed angles m and n, given that the central angle is 108 degrees.

Learn how to calculate the values of inscribed angles in a circle, using the Inscribed Angle Theorem, given a central angle of 108 degrees. Detailed explanation of key geometry principles. Suitable for students in Grades 9-10.

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