Brandon drew the following triangle.
B
C
A
Based on the diagram, which statement is true?
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.
B.
The sum of the measures of the interior and exterior angles of a triangle is always 180°.
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.
D. The sum of the measures of the interior and exterior angles of a triangle is always 360°.

The question involves the properties of the angles in a triangle and their relationships, specifically focusing on exterior and interior angles. Let's analyze each statement:

- **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 statement is **true**. In any triangle, the measure of an exterior angle is always equal to the sum of the two opposite interior angles (non-adjacent angles). This is known as the *Exterior Angle Theorem*. So, if C is the exterior angle, it will be equal to A + B.

- **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 an interior angle and its corresponding exterior angle is always 180°, but the sum of all interior and exterior angles of a triangle would be greater than 180°. For example, for each vertex, the interior and exterior angle sum is 180°, but there are three vertices.

- **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.*

  This statement is **false**. According to the Exterior Angle Theorem, the exterior angle is **equal** to the sum of the two opposite interior angles, not less than their sum.

- **Statement D**: *The sum of the measures of the interior and exterior angles of a triangle is always 360°.*

  This statement is **true**. Each pair of an interior and exterior angle at a vertex sums to 180°, and since there are three vertices in a triangle, the total sum for all interior and exterior angles is 360°.

### Conclusion:
- The correct answer is **A**.

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Would you like more details or have any questions?

### 5 Related Questions:
1. What is the Exterior Angle Theorem and how is it used in solving problems?
2. How do you find the sum of interior angles in any polygon?
3. Can a triangle have an exterior angle larger than the sum of the other two angles?
4. Why is the sum of the interior angles of a triangle always 180°?
5. How does the number of sides in a polygon affect the sum of exterior angles?

**Tip**: For any polygon, the sum of the exterior angles, one at each vertex, always adds up to 360°, regardless of the number of sides.

Brandon drew the following triangle. B C A Based on the diagram, which statement is true? 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. B. The sum of the measures of the interior and exterior angles of a triangle is always 180°. 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. D. The sum of the measures of the interior and exterior angles of a triangle is always 360°.

Explore how the Exterior Angle Theorem applies to triangles with a detailed explanation and step-by-step solution. Learn why the exterior angle of a triangle equals the sum of the opposite interior angles, and see which common misconceptions are clarified. Suitable for students in Grades 8-10.

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