Which statement regarding the interior and exterior angles of a triangle is always true?

• A. The sum of the measures of the three interior angles of a triangle is $180°$.
• B. Each exterior angle of a triangle is always equal to one of the interior angles.
• C. The sum of the measures of the three exterior angles of a triangle is $180°$.
• D. The sum of the measures of the three interior angles of a triangle is $360°$.

Answer: (A)

Verified step by step guidance

1. Recall the fundamental property of triangles: the sum of the interior angles of any triangle is always 180 degrees. This is a key fact in Euclidean geometry.
2. Understand that an exterior angle of a triangle is formed by extending one side of the triangle. The exterior angle and its adjacent interior angle are supplementary, meaning their measures add up to 180 degrees.
3. Note that each exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles, not just one interior angle. This is known as the Exterior Angle Theorem.
4. Recognize that the sum of the three exterior angles of a triangle, one at each vertex, is always 360 degrees, because they effectively form a full rotation around the triangle.
5. Therefore, the only statement that is always true is that the sum of the measures of the three interior angles of a triangle is 180 degrees.