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The image shows a geometric diagram involving a triangle inscribed in a circle, with angles labeled \( u \), \( v \), and \( w \), and an external angle of 64° formed at the point where the triangle touches the circle.

To understand the relationship between these angles:

- \( v \) is an interior angle at the center of the circle.
- \( w \) and \( u \) are the other interior angles of the triangle.
- The 64° angle outside the triangle appears to be an external angle related to angle \( v \).

We can use the fact that the sum of the interior angles of a triangle is 180°. Furthermore, the external angle theorem states that the external angle (64° here) is equal to the sum of the opposite two interior angles.

Let me know if you want detailed steps on calculating the specific angles in this triangle or related calculations.

Would you like to proceed with that or have any specific questions?

Here are 5 related questions for further exploration:
1. How can we calculate angle \( v \) using the external angle theorem?
2. What are the relationships between angles in a triangle inscribed in a circle?
3. How do we use the sum of interior angles of a triangle to find unknown angles?
4. What are the properties of external angles in any triangle?
5. How does the inscribed angle theorem relate to this problem?

**Tip:** In any triangle, the external angle is equal to the sum of the two non-adjacent interior angles. This is very helpful in solving angle problems like this one!

The diagram shows a triangle inscribed in a circle with angles labeled u, v, and w, along with an external angle of 64° outside the triangle.

Explore how to solve for the interior angles of a triangle inscribed in a circle with an external angle of 64°. Learn about the External Angle Theorem and how the sum of interior angles helps find unknown angles in geometry problems. Suitable for Grades 8-10.

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