In the context of the Law of Sines, which of the following has a measure that is equal to the sum of the measures of the interior angles of a triangle?

• A. $180°$
• B. $360°$
• C. $90°$
• D. $270°$

Answer: (A)

Verified step by step guidance

1. Recall that the Law of Sines relates the ratios of the lengths of sides of a triangle to the sines of their opposite angles, but it does not change the fundamental properties of triangle angles.
2. Understand that the sum of the interior angles of any triangle, regardless of its type, is always a constant value.
3. This constant sum is a fundamental property in Euclidean geometry and is equal to 180 degrees.
4. Review the options given: 180°, 360°, 90°, and 270°, and identify which corresponds to the sum of interior angles of a triangle.
5. Conclude that the measure equal to the sum of the interior angles of a triangle is 180°, which aligns with the Law of Sines context.