Question

102°, 36°, 42° can these form a triangle

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine if the angles 102°, 36°, and 42° can form a triangle, let's use the triangle inequality theorem.

According to the theorem, for a triangle to be formed, the sum of any two angles must be larger than the third angle.

Let's check all the possible combinations:
1. 102° + 36° = 138° (which is larger than 42°)
2. 102° + 42° = 144° (which is larger than 36°)
3. 36° + 42° = 78° (which is smaller than 102°)

Therefore, the angles 102°, 36°, and 42° cannot form a triangle since the sum of the first two angles is not larger than the third angle.

Answer 2

27°, 96°, 14°

This set forms a triangle.
This set doesn't form a triangle.

Answer 3

[AI-generated answer — Bot GPT 3.5]

To determine if the angles 27°, 96°, and 14° can form a triangle, let's use the triangle inequality theorem.

According to the theorem, for a triangle to be formed, the sum of any two angles must be larger than the third angle.

Let's check all the possible combinations:
1. 27° + 96° = 123° (which is larger than 14°)
2. 27° + 14° = 41° (which is smaller than 96°)
3. 96° + 14° = 110° (which is larger than 27°)

Therefore, the angles 27°, 96°, and 14° can form a triangle since the sum of any two angles is larger than the third angle.