A quadrilateral has three acute angles, each measuring `75^(@)`. Find the measure of the fourth angle.

Options

A. `90^(@)`
B. `75^(@)`
C. `125^(@)`
D. `135^(@)`

Answer

To find the measure of the fourth angle in a quadrilateral where three angles are given as 75 degrees each, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the properties of a quadrilateral**:
The sum of all interior angles in a quadrilateral is always 360 degrees.

2. **Identify the known angles**:
We are given three angles of the quadrilateral:
- Angle A = 75 degrees
- Angle B = 75 degrees
- Angle C = 75 degrees

3. **Calculate the sum of the known angles**:
To find the sum of the three known angles:
\[ \text{Sum of angles A, B, and C} = 75 + 75 + 75 = 225 \text{ degrees} \]

4. **Set up the equation for the fourth angle**:
Let the fourth angle be denoted as Angle D. According to the property of quadrilaterals:
\[ \text{Angle A} + \text{Angle B} + \text{Angle C} + \text{Angle D} = 360 \text{ degrees} \]
Substituting the known values:
\[ 225 + \text{Angle D} = 360 \]

5. **Solve for the fourth angle**:
To find Angle D, subtract the sum of the three angles from 360 degrees:
\[ \text{Angle D} = 360 - 225 = 135 \text{ degrees} \]

### Conclusion:
The measure of the fourth angle in the quadrilateral is **135 degrees**.

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