Brandon drew the following triangle.
 


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 correct answer is **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.**

### Explanation:
- The **exterior angle theorem** states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles (the remote interior angles).
- In this case, if angle \( C \) is the exterior angle, then its measure is equal to the sum of the measures of angles \( A \) and \( B \), which are the two remote interior angles.

#### Incorrect Answers:
- **B.** The sum of an interior and exterior angle on the same vertex is always \( 180^\circ \), but the sum of all interior and exterior angles of a triangle is not always \( 180^\circ \).
- **C.** The measure of the exterior angle is actually equal to (not less than) the sum of the remote interior angles.
- **D.** The sum of the exterior angles of any polygon is always \( 360^\circ \), but this does not apply to the interior and exterior angles together in this way.

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### Related Questions:
1. What is the sum of the interior angles of a triangle?
2. How can you find the exterior angle of a triangle given two interior angles?
3. What is the sum of the exterior angles of any polygon?
4. How do we prove the exterior angle theorem using algebra?
5. Can an exterior angle of a triangle be less than the sum of the interior angles?

**Tip:** Remember that the sum of the interior angles of any triangle is always 180°.

Brandon drew the following triangle. 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 to apply the exterior angle theorem to find the exterior angle of a triangle. This problem explains how the measure of an exterior angle is equal to the sum of the two remote interior angles. Ideal for students in Grades 6-8 learning about triangles and angle relationships.

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