According to the Law of Sines, under which of the following angle conditions could a triangle exist? Select the correct option.

• A. The sum of the three angles is $200°$.
• B. The sum of the three angles is less than $180°$.
• C. The sum of the three angles is $180°$ and each angle is greater than $0°$.
• D. One angle is $0°$.

Answer: (C)

Verified step by step guidance

1. Recall the fundamental property of triangles: the sum of the three interior angles must be exactly \$180^\circ$.
2. Understand that the Law of Sines applies to any triangle, but for a triangle to exist, each angle must be greater than \$0^\circ\( and less than \)180^\circ$.
3. Evaluate the given conditions: if the sum of angles is \$200^\circ$, it violates the triangle angle sum property, so no triangle can exist.
4. If the sum of angles is less than \$180^\circ$, it also violates the triangle angle sum property, so no triangle can exist.
5. If one angle is \$0^\circ$, the figure is not a triangle because an angle of zero means no interior angle at that vertex, so no triangle can exist.