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, 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 always equal to 360 degrees.

2. **Identify the Given Angles**:
The three angles provided are:
- Angle A = 75 degrees
- Angle B = 90 degrees
- Angle C = 75 degrees

3. **Set Up the Equation**:
Let the fourth angle be Angle D. According to the property of quadrilaterals, we can write the equation:
\[ \text{Angle A} + \text{Angle B} + \text{Angle C} + \text{Angle D} = 360^\circ \]
Substituting the known values:
\[ 75 + 90 + 75 + \text{Angle D} = 360 \]

4. **Calculate the Sum of the Known Angles**:
First, we add the three known angles:
\[ 75 + 90 = 165 \]
\[ 165 + 75 = 240 \]
So, the sum of the three angles is 240 degrees.

5. **Solve for the Fourth Angle**:
Now, we can substitute this sum back into the equation:
\[ 240 + \text{Angle D} = 360 \]
To find Angle D, we subtract 240 from both sides:
\[ \text{Angle D} = 360 - 240 \]
\[ \text{Angle D} = 120 \]

6. **Conclusion**:
Therefore, the fourth angle of the quadrilateral is 120 degrees.

### Final Answer:
The fourth angle is 120 degrees.

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