Three angles of a quadrilateral are `75^(@), 90^(@) and 75^(@)`. Find the measure of the fourth angle.

Answer

To find the measure of the fourth angle in a quadrilateral when three angles are given, 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 360 degrees.

2. **Identify the Given Angles**:
The angles provided are:
- First angle = 75 degrees
- Second angle = 90 degrees
- Third angle = 75 degrees

3. **Let the Fourth Angle be x**:
We can denote the fourth angle as \( x \).

4. **Set Up the Equation**:
According to the property of quadrilaterals, we can write the equation:
\[ 75 + 90 + 75 + x = 360 \]

5. **Calculate the Sum of the Given Angles**:
First, we need to add the three angles:
\[ 75 + 90 + 75 = 240 \]

6. **Substitute the Sum Back into the Equation**:
Now, substitute the sum back into the equation:
\[ 240 + x = 360 \]

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

8. **Conclusion**:
Therefore, the measure of the fourth angle is \( 120 \) degrees.

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

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