If the sum of two angles is equal to an obtuse angle, then which of the following is not possible ?

Options

A. One obtuse and one acute angle
B. One right angle and one acute angle
C. Two acute angles
D. Two right angles

Answer

To solve the problem, we need to determine which of the given options cannot yield a sum that is an obtuse angle when two angles are added together. An obtuse angle is defined as an angle that is greater than 90 degrees but less than 180 degrees.

### Step-by-Step Solution:

1. **Understanding the Definition of Angles**:
- An obtuse angle is any angle that measures more than 90 degrees and less than 180 degrees.

2. **Analyzing Possible Combinations**:
- We need to consider combinations of angles: obtuse, acute, and right angles.

3. **Combination of One Obtuse Angle and One Acute Angle**:
- If we take one obtuse angle (e.g., 120 degrees) and one acute angle (e.g., 30 degrees), their sum is 150 degrees, which is an obtuse angle. This combination is possible.

4. **Combination of One Right Angle and One Acute Angle**:
- A right angle is 90 degrees. If we add a right angle (90 degrees) to an acute angle (e.g., 30 degrees), the sum is 120 degrees, which is also an obtuse angle. This combination is possible.

5. **Combination of Two Acute Angles**:
- If we take two acute angles (e.g., 70 degrees and 78 degrees), their sum is 148 degrees, which is an obtuse angle. This combination is possible.

6. **Combination of Two Right Angles**:
- If we take two right angles (90 degrees + 90 degrees), their sum is 180 degrees, which is a straight angle, not an obtuse angle. Therefore, this combination is **not possible**.

### Conclusion:
The combination of two right angles cannot yield an obtuse angle, making it the option that is not possible.