Which set of three angles could represent the interior angles of a triangle?

• A. $60°$, $60°$, $60°$
• B. $90°$, $90°$, $0°$
• C. $90°$, $45°$, $60°$
• D. $100°$, $40°$, $50°$

Answer: (A)

Verified step by step guidance

1. Recall the fundamental property of the interior angles of a triangle: the sum of the three interior angles must be exactly \(180^\circ\).
2. For each given set of angles, add the three angles together using the formula \(\text{Sum} = \alpha + \beta + \gamma\), where \(\alpha\), \(\beta\), and \(\gamma\) are the angles in degrees.
3. Check the first set: \(60^\circ + 60^\circ + 60^\circ\). Calculate their sum to see if it equals \(180^\circ\).
4. Check the second set: \(90^\circ + 90^\circ + 0^\circ\). Calculate their sum and verify if it equals \(180^\circ\).
5. Repeat the process for the third and fourth sets: \(90^\circ + 45^\circ + 60^\circ\) and \(100^\circ + 40^\circ + 50^\circ\), respectively, to determine which sets satisfy the triangle angle sum property.