Which of the following sets of angles can be used to construct a triangle?

• A. $60°$, $70°$, $50°$
• B. $100°$, $50°$, $40°$
• C. $120°$, $30°$, $40°$
• D. $90°$, $60°$, $40°$

Answer: (A)

Verified step by step guidance

1. Recall the Triangle Angle Sum Theorem, which states that the sum of the interior angles of a triangle must be exactly \$180^\circ$.
2. For each 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 if the sum of the angles in each set equals \$180^\circ\(. If the sum is exactly \)180^\circ$, then the set of angles can form a triangle.
4. Verify that each individual angle is greater than \$0^\circ$ because angles must be positive to form a valid triangle.
5. Conclude which sets satisfy both conditions: sum equals \$180^\circ$ and all angles are positive, indicating those sets can be used to construct a triangle.