To determine which of the given statements is correct regarding angles forming a linear pair, we will analyze each statement step by step.
### Step-by-Step Solution:
1. **Understanding Linear Pair of Angles**:
A linear pair of angles consists of two adjacent angles formed when two lines intersect. The sum of the angles in a linear pair is always 180 degrees.
2. **Analyzing Statement 1**:
- Statement: "Two angles forming a linear pair can each be 90 degrees."
- If both angles are 90 degrees, then their sum would be 90 + 90 = 180 degrees, which is correct. However, this is not the only possibility for angles forming a linear pair. Therefore, this statement is not universally correct.
3. **Analyzing Statement 2**:
- Statement: "Two angles forming a linear pair can both be acute."
- If both angles are acute, their measures would be less than 90 degrees. For example, if both angles are 89 degrees, their sum would be 89 + 89 = 178 degrees, which is less than 180 degrees. Hence, this statement is incorrect.
4. **Analyzing Statement 3**:
- Statement: "Two angles forming a linear pair can both be obtuse."
- If both angles are obtuse, their measures would be greater than 90 degrees. For example, if both angles are 91 degrees, their sum would be 91 + 91 = 182 degrees, which exceeds 180 degrees. Thus, this statement is also incorrect.
5. **Analyzing Statement 4**:
- Statement: "The bisector of the adjacent angles forming a linear pair forms a right angle."
- When a line bisects two adjacent angles that form a linear pair, each angle is divided into two equal parts. Since the sum of the angles is 180 degrees, if the bisector divides them equally, each angle will be 90 degrees. Therefore, this statement is correct.
### Conclusion:
The correct statement among the options provided is:
**"The bisector of the adjacent angles forming a linear pair forms a right angle."**
