In `DeltaABC`, if `angleAltangleBlt45^(@)`, then ABC is a/an _______ triangle .

Answer

To determine the type of triangle ABC given that angle A is less than angle B and both angles are less than 45 degrees, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Angles**: We know that in triangle ABC, angle A < angle B and both angles are less than 45 degrees. This means:
- Angle A < 45°
- Angle B < 45°

2. **Sum of Angles in a Triangle**: The sum of the angles in any triangle is always 180 degrees. Therefore, we can write:
\[ \text{Angle A} + \text{Angle B} + \text{Angle C} = 180° \]

3. **Finding the Upper Limit for Angles A and B**: Since both angle A and angle B are less than 45 degrees, we can add these two angles:
\[ \text{Angle A} + \text{Angle B} < 45° + 45° = 90° \]
This means:
\[ \text{Angle A} + \text{Angle B} < 90° \]

4. **Calculating Angle C**: Now, if we substitute the sum of angles A and B into the triangle angle sum equation:
\[ \text{Angle C} = 180° - (\text{Angle A} + \text{Angle B}) \]
Since we established that angle A + angle B < 90°, we can say:
\[ \text{Angle C} > 180° - 90° = 90° \]

5. **Conclusion about Triangle ABC**: Since angle C is greater than 90 degrees, triangle ABC is classified as an obtuse triangle.

Thus, the answer is: **ABC is an obtuse triangle**.