Three angles of a quadrilateral are `75^(@),90^(@) and 75^(@)`, then the fourth angle is

Options

A. `90^(@)`
B. `95^(@)`
C. `105^(@)`
D. `120^(@)`

Explanation

To find the fourth angle of the quadrilateral when three angles are given as \(75^\circ\), \(90^\circ\), and \(75^\circ\), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Sum of Angles in a Quadrilateral**:
The sum of all interior angles in a quadrilateral is \(360^\circ\).

2. **List the Known Angles**:
We have three angles:
- Angle 1 = \(75^\circ\)
- Angle 2 = \(90^\circ\)
- Angle 3 = \(75^\circ\)

3. **Set Up the Equation**:
Let the fourth angle be \(x\). According to the property of quadrilaterals, we can write the equation:
\[ 75^\circ + 90^\circ + 75^\circ + x = 360^\circ \]

4. **Combine the Known Angles**:
First, we add the known angles together:
\[ 75^\circ + 90^\circ + 75^\circ = 240^\circ \]

5. **Substitute Back into the Equation**:
Now, substitute this sum back into the equation:
\[ 240^\circ + x = 360^\circ \]

6. **Solve for \(x\)**:
To find \(x\), subtract \(240^\circ\) from both sides:
\[ x = 360^\circ - 240^\circ \]
\[ x = 120^\circ \]

7. **Conclusion**:
Therefore, the fourth angle of the quadrilateral is \(120^\circ\).

### Final Answer:
The fourth angle is \(120^\circ\).