If three angles of a quadrilateral are each equal to `75°`, the fourth angle is

Options

A. `150°`
B. `135°`
C. `45°`
D. `75°`

Answer

To find the fourth angle of a quadrilateral when three angles are given as 75°, we can follow these steps:

### Step-by-step Solution:

1. **Identify the sum of angles in a quadrilateral**:
The sum of all interior angles in a quadrilateral is always 360°.

2. **List the known angles**:
We know that three angles are each 75°. So, we can denote the angles as:
- Angle A = 75°
- Angle B = 75°
- Angle C = 75°

3. **Calculate the sum of the known angles**:
Now, we need to find the total of the three angles:
\[ \text{Sum of known angles} = 75° + 75° + 75° = 225° \]

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

5. **Solve for Angle D**:
To find Angle D, we rearrange the equation:
\[ \text{Angle D} = 360° - 225° \]
\[ \text{Angle D} = 135° \]

### Final Answer:
The fourth angle of the quadrilateral is **135°**.

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