Question

Under which angle conditions could a triangle exist? Check all that apply.

3 acute angles
2 acute angles, 1 right angle
1 acute angle, 1 right angle, 1 obtuse angle
1 acute angle, 2 obtuse angles
2 acute angles, 1 obtuse angle

Answer 1

Possible:
- 3 acute angles — yes (e.g. 60°, 60°, 60°).
- 2 acute angles, 1 right angle — yes (right = 90°, the other two sum to 90° and can both be <90).
- 2 acute angles, 1 obtuse angle — yes (obtuse >90°, the two acutes can sum to <90°, e.g. 100°, 40°, 40°).

Not possible:
- 1 acute, 1 right, 1 obtuse — no (right 90° + obtuse >90° already exceed 180°).
- 1 acute, 2 obtuse — no (two obtuse angles >90° each would sum to >180°).