Classify the angles whose magnitudes are given below: (i) `30^(@)` (ii) ` 91^@` (iii) `179^@` (iv) `90^@` (v) `181^@` (vi) `360^@` (vii) `128^@` (viii) `(90.5)^@` (ix) `(38.3)^@` (x) `80^@` (xi) `0^@` (xii) `15^@`

Answer

To classify the angles based on their magnitudes, we will follow the definitions of different types of angles:

1. **Acute Angle**: An angle that is less than 90 degrees.
2. **Right Angle**: An angle that is exactly 90 degrees.
3. **Obtuse Angle**: An angle that is greater than 90 degrees but less than 180 degrees.
4. **Straight Angle**: An angle that is exactly 180 degrees.
5. **Reflex Angle**: An angle that is greater than 180 degrees but less than 360 degrees.
6. **Complete Angle**: An angle that is exactly 360 degrees.

Now, let's classify each angle step by step:

### Step-by-Step Classification:

(i) **30°**:
- This angle is less than 90 degrees.
- **Classification**: Acute Angle.

(ii) **91°**:
- This angle is greater than 90 degrees but less than 180 degrees.
- **Classification**: Obtuse Angle.

(iii) **179°**:
- This angle is also greater than 90 degrees but less than 180 degrees.
- **Classification**: Obtuse Angle.

(iv) **90°**:
- This angle is exactly 90 degrees.
- **Classification**: Right Angle.

(v) **181°**:
- This angle is greater than 180 degrees but less than 360 degrees.
- **Classification**: Reflex Angle.

(vi) **360°**:
- This angle is exactly 360 degrees.
- **Classification**: Complete Angle.

(vii) **128°**:
- This angle is greater than 90 degrees but less than 180 degrees.
- **Classification**: Obtuse Angle.

(viii) **90.5°**:
- This angle is greater than 90 degrees but less than 180 degrees.
- **Classification**: Obtuse Angle.

(ix) **38.3°**:
- This angle is less than 90 degrees.
- **Classification**: Acute Angle.

(x) **80°**:
- This angle is less than 90 degrees.
- **Classification**: Acute Angle.

(xi) **0°**:
- This angle is exactly 0 degrees.
- **Classification**: Zero Angle.

(xii) **15°**:
- This angle is less than 90 degrees.
- **Classification**: Acute Angle.

### Summary of Classifications:
1. 30° - Acute Angle
2. 91° - Obtuse Angle
3. 179° - Obtuse Angle
4. 90° - Right Angle
5. 181° - Reflex Angle
6. 360° - Complete Angle
7. 128° - Obtuse Angle
8. 90.5° - Obtuse Angle
9. 38.3° - Acute Angle
10. 80° - Acute Angle
11. 0° - Zero Angle
12. 15° - Acute Angle