Which of the following is true for a triangle ?

Question

Accepted Answer

Option 4 is the correct answer: "One angle is always an acute angle."

### Explanation for Option 4:

In any triangle, the sum of the interior angles is always 180 degrees. An acute angle is defined as an angle that is less than 90 degrees. In a triangle, it is always possible to have at least one angle that is less than 90 degrees, making it an acute angle. This is true for all types of triangles, whether they are acute, right, or obtuse triangles.

- **Acute Triangle:** All three angles are acute, so clearly, at least one angle is acute.
- **Right Triangle:** One angle is exactly 90 degrees, and the other two angles must be acute to sum up to 180 degrees.
- **Obtuse Triangle:** One angle is greater than 90 degrees, but the other two angles must be acute to ensure the total is 180 degrees.

Thus, in every triangle, there is always at least one acute angle, supporting the correctness of Option 4.

### Explanation for why other options are incorrect:

1. **Option 1: All the angles are always acute angle**
   - This is incorrect because not all triangles have all acute angles. For example, right triangles have one right angle, and obtuse triangles have one obtuse angle. Therefore, not all angles in every triangle can be acute.

2. **Option 2: One angle is always a right angle**
   - This is incorrect because only right triangles have a right angle. Other types of triangles, such as acute and obtuse triangles, do not have a right angle.

3. **Option 3: One angle is always an obtuse angle**
   - This is incorrect because only obtuse triangles have an obtuse angle. Acute and right triangles do not have an obtuse angle.

By focusing on the properties of different types of triangles, it is clear that Option 4 is the only universally true statement for all triangles.