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The problem in the image asks which statement is true based on the diagram of a triangle with an exterior angle labeled \( C \) and two interior angles labeled \( A \) and \( B \).

### Let's evaluate the provided statements:

1. **Statement A**: "The measure of an exterior angle of a triangle, angle C, is equal to the sum of the measures of angle A and angle B."
   - **This is true**. According to the Exterior Angle Theorem, the measure of an exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles. Therefore, \( C = A + B \).

2. **Statement B**: "The sum of the measures of the interior and exterior angles of a triangle is always 180°."
   - This statement is **false**. The sum of the interior angles of a triangle is always 180°, but when including an exterior angle, the total will exceed 180°.

3. **Statement C**: "The measure of an exterior angle of a triangle, angle C, is less than the sum of the measures of angle A and angle B."
   - **False**, as explained earlier. The measure of angle \( C \) is **equal** to the sum of \( A \) and \( B \), not less than.

4. **Statement D**: "The sum of the measures of the interior and exterior angles of a triangle is always 360°."
   - **True** if interpreted as the sum of one exterior angle for each interior angle, since the exterior angle forms a linear pair with an interior angle. In that case, the total around the triangle (interior + exterior) would be 360°.

### Correct Answer: **A**. 

This is the most directly accurate based on the Exterior Angle Theorem.

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Would you like more details on how the Exterior Angle Theorem works or clarification on any other statement?

Here are 5 related questions to think about:
1. What is the sum of the interior angles in any triangle?
2. Can an exterior angle of a triangle ever be smaller than both interior angles?
3. How would the angle sums change if the figure were a quadrilateral?
4. What is the relationship between supplementary angles and the exterior angle of a triangle?
5. How can the Exterior Angle Theorem be applied to solve problems involving missing angles?

**Tip**: Always remember, the exterior angle of a triangle is equal to the sum of the opposite two interior angles.

Based on the diagram, which statement is true?

Determine the correct statement about triangle angles based on the Exterior Angle Theorem. Learn how an exterior angle equals the sum of the two opposite interior angles. Suitable for students in Grades 7-9.

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