Question

Which set of degrees can be the measures of angles in a triangle? Select all that apply.
32, 84, 64
115, 40, 25
90, 27, 100

Answer 1

To determine whether a set of degrees can be the measures of angles in a triangle, we need to check two conditions:

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

Let's evaluate each set of angles:

1. **32, 84, 64**:
- Sum: 32 + 84 + 64 = 180 degrees (valid)
- All angles are greater than 0 (valid)
- This set is valid.

2. **115, 40, 25**:
- Sum: 115 + 40 + 25 = 180 degrees (valid)
- All angles are greater than 0 (valid)
- This set is valid.

3. **90, 27, 100**:
- Sum: 90 + 27 + 100 = 217 degrees (invalid)
- Although all angles are greater than 0, the sum exceeds 180 degrees.
- This set is not valid.

Based on this analysis, the valid sets of angles that can be measures of angles in a triangle are:
- **32, 84, 64**
- **115, 40, 25**