Which of the following sets of angles could form a triangle? Select all that apply.

Question

(4 Points)

30°, 60°, 80°

45°, 45°, 100°

90°, 45°, 45°

50°, 50°, 80°

Answer 1

To determine which sets of angles can form a triangle, they must satisfy two conditions:

1. The sum of the angles must be exactly 180°.
2. Each angle must be greater than 0°.

Let's examine each set of angles:

1. 30°, 60°, 80°

   • Sum: 30° + 60° + 80° = 170°
   • Does not satisfy the angle sum condition.

2. 45°, 45°, 100°

   • Sum: 45° + 45° + 100° = 190°
   • Does not satisfy the angle sum condition.

3. 90°, 45°, 45°

   • Sum: 90° + 45° + 45° = 180°
   • Satisfies the angle sum condition; all angles are greater than 0°.

4. 50°, 50°, 80°

   • Sum: 50° + 50° + 80° = 180°
   • Satisfies the angle sum condition; all angles are greater than 0°.

Based on this analysis, the sets of angles that could form a triangle are:

• 90°, 45°, 45°
• 50°, 50°, 80°