Which of the following lists of angle measures could be the angle measures of a triangle?

• A. $90°$, $45°$, $60°$
• B. $60°$, $60°$, $60°$
• C. $100°$, $40°$, $50°$
• D. $120°$, $30°$, $40°$

Answer: (C)

Verified step by step guidance

1. Recall the fundamental property of triangles: the sum of the interior angles must be exactly \$180^\circ$.
2. For each given list of angles, add the three angle measures together to check if their sum equals \$180^\circ$.
3. Check the first list: \$90^\circ + 45^\circ + 60^\circ = 195^\circ\(, which is greater than \)180^\circ$, so this cannot be the angles of a triangle.
4. Check the second list: \$60^\circ + 60^\circ + 60^\circ = 180^\circ$, which satisfies the triangle angle sum property, so this could be the angles of a triangle.
5. Check the third list: \$100^\circ + 40^\circ + 50^\circ = 190^\circ\(, which is greater than \)180^\circ$, so this cannot be the angles of a triangle.