Question

Which cannot be the angle measurements of triangle ABC?
Measure of angle A = 55 degrees, measure of angle B = 65 degrees, measure of angle C = 60 degrees
Measure of angle A = 60 degrees, measure of angle B = 60 degrees, measure of angle C = 60 degrees
Measure of angle A = 57 degrees, measure of angle B = 58 degrees, measure of angle C = 65 degrees
Measure of angle A = 61 degrees, measure of angle B = 57 degrees, measure of angle C = 61 degrees

Answer 1

To determine which set of angle measurements cannot represent a triangle, we need to apply the triangle inequality theorem, specifically the rule that the sum of the angles in any triangle must equal 180 degrees.

Let's check the measurements provided for each option:

1. **Measure of angle A = 55 degrees, measure of angle B = 65 degrees, measure of angle C = 60 degrees**
- Sum: 55 + 65 + 60 = 180 degrees (valid triangle)

2. **Measure of angle A = 60 degrees, measure of angle B = 60 degrees, measure of angle C = 60 degrees**
- Sum: 60 + 60 + 60 = 180 degrees (valid triangle)

3. **Measure of angle A = 57 degrees, measure of angle B = 58 degrees, measure of angle C = 65 degrees**
- Sum: 57 + 58 + 65 = 180 degrees (valid triangle)

4. **Measure of angle A = 61 degrees, measure of angle B = 57 degrees, measure of angle C = 61 degrees**
- Sum: 61 + 57 + 61 = 179 degrees (invalid triangle)

Based on this analysis, the fourth set of angle measurements cannot represent a triangle. Thus, the answer is:
**Measure of angle A = 61 degrees, measure of angle B = 57 degrees, measure of angle C = 61 degrees**.