A quadrilateral has three acute angles each measuring `70^(@)` . The measure of fourth angle is

Options

A. `140^(@)`
B. `150^(@)`
C. `105^(@)`
D. `120^(@)`

Answer

To find the measure of the fourth angle in a quadrilateral where three angles each measure \(70^\circ\), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Angles**:
We know that in the quadrilateral ABCD, the angles are:
- Angle A = \(70^\circ\)
- Angle B = \(70^\circ\)
- Angle C = \(70^\circ\)
- Angle D = ?

2. **Use the Sum of Angles in a Quadrilateral**:
The sum of all angles in a quadrilateral is \(360^\circ\). Therefore, we can write the equation:
\[ \text{Angle A} + \text{Angle B} + \text{Angle C} + \text{Angle D} = 360^\circ \]

3. **Substitute Known Values**:
Substitute the values of angles A, B, and C into the equation:
\[ 70^\circ + 70^\circ + 70^\circ + \text{Angle D} = 360^\circ \]

4. **Calculate the Sum of Known Angles**:
Add the three angles together:
\[ 70^\circ + 70^\circ + 70^\circ = 210^\circ \]
So, we have:
\[ 210^\circ + \text{Angle D} = 360^\circ \]

5. **Isolate Angle D**:
To find Angle D, subtract \(210^\circ\) from \(360^\circ\):
\[ \text{Angle D} = 360^\circ - 210^\circ \]

6. **Perform the Calculation**:
\[ \text{Angle D} = 150^\circ \]

### Final Answer:
The measure of the fourth angle \(D\) is \(150^\circ\).