Can two angles be supplementary, if both of them be

Options

A. obtuse
B. right
C. acute
D. none of these

Answer

To determine whether two angles can be supplementary when both are obtuse, right, or acute, we need to understand the definitions of these types of angles and the concept of supplementary angles.

### Step-by-Step Solution:

1. **Understanding Supplementary Angles**:
- Supplementary angles are two angles whose sum is exactly 180 degrees.

2. **Understanding Obtuse Angles**:
- An obtuse angle is an angle that is greater than 90 degrees but less than 180 degrees (i.e., 90° < angle < 180°).

3. **Checking if Two Obtuse Angles Can Be Supplementary**:
- If we take two obtuse angles, since both are greater than 90 degrees, their sum will be:
- For example, if we take two obtuse angles, say 100° and 110°, the sum is 100° + 110° = 210°.
- Since the sum of two obtuse angles is always greater than 180 degrees, **two obtuse angles cannot be supplementary**.

4. **Understanding Right Angles**:
- A right angle is exactly 90 degrees.

5. **Checking if Two Right Angles Can Be Supplementary**:
- If we take two right angles, their sum is:
- 90° + 90° = 180°.
- Therefore, **two right angles can be supplementary**.

6. **Understanding Acute Angles**:
- An acute angle is an angle that is less than 90 degrees (i.e., 0° < angle < 90°).

7. **Checking if Two Acute Angles Can Be Supplementary**:
- If we take two acute angles, their sum will always be less than 180 degrees:
- For example, if we take two acute angles, say 30° and 40°, the sum is 30° + 40° = 70°.
- Since the sum of two acute angles is always less than 180 degrees, **two acute angles cannot be supplementary**.

### Conclusion:
- **Two obtuse angles cannot be supplementary.**
- **Two right angles can be supplementary.**
- **Two acute angles cannot be supplementary.**