The three angles of a quadrilateral are `80^(@),70^(@)and120^(@)`. The fourth angle is

Options

A. `110^(@)`
B. `100^(@)`
C. `90^(@)`
D. `80^(@)`

Answer

To find the fourth angle of the quadrilateral, 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. **List the known angles**: We are given three angles of the quadrilateral:
- Angle 1 = 80 degrees
- Angle 2 = 70 degrees
- Angle 3 = 120 degrees

3. **Set up the equation**: Let the fourth angle be represented as \( x \). According to the property of quadrilaterals, we can write the equation:
\[ 80 + 70 + 120 + x = 360 \]

4. **Calculate the sum of the known angles**: Add the three angles together:
\[ 80 + 70 = 150 \]
\[ 150 + 120 = 270 \]

5. **Substitute the sum back into the equation**: Now we can substitute the sum of the known angles back into the equation:
\[ 270 + x = 360 \]

6. **Solve for \( x \)**: To find the value of \( x \), subtract 270 from both sides:
\[ x = 360 - 270 \]
\[ x = 90 \]

7. **Conclusion**: The fourth angle of the quadrilateral is \( 90 \) degrees.

### Final Answer:
The fourth angle is \( 90^\circ \).