Classify the angles as acute, right, obtuse, straight, reflex or complete based on their measures given below.
a. `289^(@)`.
b. `76^(@)`.
c. `180^(@)`.
d. `90^(@)`.
e. `311^(@)`.
f. `145^(@)`
g. `360^(@)`.

Answer

To classify the angles based on their measures, we will use the definitions of different types of angles:

1. **Acute Angle**: An angle that measures less than 90 degrees (0° < angle < 90°).
2. **Right Angle**: An angle that measures exactly 90 degrees (angle = 90°).
3. **Obtuse Angle**: An angle that measures more than 90 degrees but less than 180 degrees (90° < angle < 180°).
4. **Straight Angle**: An angle that measures exactly 180 degrees (angle = 180°).
5. **Reflex Angle**: An angle that measures more than 180 degrees but less than 360 degrees (180° < angle < 360°).
6. **Complete Angle**: An angle that measures exactly 360 degrees (angle = 360°).

Now, let's classify each angle given in the question:

### Step-by-Step Classification:

**a. 289°**
- 289° is greater than 180° and less than 360°.
- **Classification**: Reflex Angle

**b. 76°**
- 76° is less than 90°.
- **Classification**: Acute Angle

**c. 180°**
- 180° is exactly equal to 180°.
- **Classification**: Straight Angle

**d. 90°**
- 90° is exactly equal to 90°.
- **Classification**: Right Angle

**e. 311°**
- 311° is greater than 180° and less than 360°.
- **Classification**: Reflex Angle

**f. 145°**
- 145° is greater than 90° but less than 180°.
- **Classification**: Obtuse Angle

**g. 360°**
- 360° is exactly equal to 360°.
- **Classification**: Complete Angle

### Summary of Classifications:
- a. 289° - Reflex Angle
- b. 76° - Acute Angle
- c. 180° - Straight Angle
- d. 90° - Right Angle
- e. 311° - Reflex Angle
- f. 145° - Obtuse Angle
- g. 360° - Complete Angle