The three angles of a quadrilateral are `76^(@), 54^(@) and 108^(@)`. Find the measure of the fourth angle.

Options

A. `85^(@)`
B. `90^(@)`
C. `122^(@)`
D. `154^(@)`

Answer

To find the measure of the fourth angle of the quadrilateral, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given angles**:
- Angle A = 76°
- Angle B = 54°
- Angle C = 108°

2. **Recall the property of quadrilaterals**:
- The sum of all angles in a quadrilateral is 360°.

3. **Set up the equation**:
- Let Angle D be the fourth angle. According to the property, we can write the equation:
\[ \text{Angle A} + \text{Angle B} + \text{Angle C} + \text{Angle D} = 360° \]
- Substituting the known values:
\[ 76° + 54° + 108° + \text{Angle D} = 360° \]

4. **Calculate the sum of the known angles**:
- First, add the three angles:
\[ 76° + 54° + 108° = 238° \]

5. **Substitute the sum back into the equation**:
- Now, we can rewrite the equation:
\[ 238° + \text{Angle D} = 360° \]

6. **Solve for Angle D**:
- To find Angle D, subtract 238° from 360°:
\[ \text{Angle D} = 360° - 238° = 122° \]

7. **Conclusion**:
- The measure of the fourth angle (Angle D) is 122°.

### Final Answer:
The measure of the fourth angle is **122°**.