State which of the following statements are true and which are false :
A triangle cannot have more than one obtuse angle .

Answer

To determine whether the statement "A triangle cannot have more than one obtuse angle" is true or false, we can analyze the properties of triangles and angles.

### Step-by-Step Solution:

1. **Understanding the Definition of an Obtuse Angle**:
An obtuse angle is defined as an angle that measures greater than 90 degrees but less than 180 degrees.

2. **Sum of Angles in a Triangle**:
The sum of all angles in a triangle is always 180 degrees. This is a fundamental property of triangles.

3. **Assuming Two Obtuse Angles**:
Let's assume that a triangle has two obtuse angles. For example, let’s say angle A and angle B are both obtuse angles.
- If angle A is greater than 90 degrees (let's say 100 degrees) and angle B is also greater than 90 degrees (let's say 100 degrees), we can add these two angles together.

4. **Calculating the Total**:
- Angle A + Angle B = 100 degrees + 100 degrees = 200 degrees.

5. **Finding the Third Angle**:
- Now, we need to find angle C to satisfy the triangle angle sum property:
- Angle A + Angle B + Angle C = 180 degrees.
- Therefore, 200 degrees + Angle C = 180 degrees.

6. **Conclusion**:
- This leads to an impossible situation because if we subtract 200 degrees from both sides, we find that Angle C would have to be -20 degrees, which is not possible.
- Hence, it is impossible for a triangle to have more than one obtuse angle.

### Final Answer:
The statement "A triangle cannot have more than one obtuse angle" is **True**.

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