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To prove that the sum of the exterior angles of a triangle is 360°, we can follow a logical geometric construction using a simple diagram.

### Steps to draw and explain the diagram:
1. **Draw a triangle**: Start by drawing any triangle \( \triangle ABC \) with vertices \( A \), \( B \), and \( C \).
   
2. **Extend the sides**: Extend each of the sides of the triangle beyond the vertices to form the exterior angles. Let the extensions at points \( A \), \( B \), and \( C \) create exterior angles \( \theta_A \), \( \theta_B \), and \( \theta_C \).

3. **Label the exterior angles**: The exterior angles at each vertex can be labeled:
   - \( \theta_A \) at vertex \( A \),
   - \( \theta_B \) at vertex \( B \),
   - \( \theta_C \) at vertex \( C \).

4. **Sum of angles**: Each exterior angle is supplementary to the interior angle of the triangle at the same vertex. Since the sum of the interior angles of a triangle is always 180°, we know:
   \[
   \theta_A + \theta_B + \theta_C = 360^\circ
   \]
   This occurs because each pair of adjacent angles (interior and exterior) forms a straight line, which sums to 180°.

Thus, the sum of the exterior angles of any triangle is always \( 360^\circ \), regardless of the shape of the triangle.

Would you like me to provide more details or clarify any step?

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Here are 5 related questions for further practice:
1. What is the sum of the interior angles of a triangle?
2. How can we prove that the sum of the angles in a quadrilateral is 360°?
3. What are the supplementary angles in a polygon, and how do they relate to exterior angles?
4. How does the sum of the exterior angles change for polygons with more than 3 sides?
5. How does extending more sides in different polygons affect the sum of the exterior angles?

### Tip:
Remember, the sum of the exterior angles of any polygon (no matter how many sides) is always 360°.

Draw a diagram to prove that the exterior angle sum of a triangle is 360°.

Learn how to prove that the sum of the exterior angles of a triangle is always 360° using a diagram. This geometric proof covers the exterior angle theorem and is suitable for students in Grades 6-8.

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