The measure of an obtuse angle `lt 90^(@)`.

Answer

To solve the question regarding the measure of an obtuse angle, we need to clarify what an obtuse angle is.

### Step-by-Step Solution:

1. **Definition of an Angle**: An angle is formed by two rays that share a common endpoint (the vertex). The measure of an angle is typically expressed in degrees.

2. **Understanding Angle Types**: There are different types of angles based on their measures:
- Acute Angle: Less than 90 degrees
- Right Angle: Exactly 90 degrees
- Obtuse Angle: Greater than 90 degrees but less than 180 degrees
- Straight Angle: Exactly 180 degrees

3. **Focus on Obtuse Angles**: An obtuse angle is defined specifically as an angle that is greater than 90 degrees and less than 180 degrees.

4. **Evaluating the Statement**: The statement in the question claims that the measure of an obtuse angle is less than 90 degrees. We need to evaluate this claim:
- Since we know that obtuse angles are defined as being greater than 90 degrees, the statement is incorrect.

5. **Conclusion**: Therefore, the measure of an obtuse angle is not less than 90 degrees; it is, in fact, greater than 90 degrees.

### Final Answer:
The statement "The measure of an obtuse angle is less than 90 degrees" is **false**. An obtuse angle is always greater than 90 degrees and less than 180 degrees.