The sum of the four angles of a quadrilateral is `360^(@)`.
Three angles of a quadrilateral are respectively equal to `110^(@), 50^(@) and 40^(@)` . Find its fourth angle.

Options

A. `160^(@)`
B. `120^(@)`
C. `80^(@)`
D. `140^(@)`

Answer

To find the fourth angle of the quadrilateral, we can follow these steps:

### Step 1: Understand the property of quadrilaterals
The sum of the four angles in a quadrilateral is always \(360^\circ\).

### Step 2: Write down the known angles
The three angles given are:
- Angle 1 = \(110^\circ\)
- Angle 2 = \(50^\circ\)
- Angle 3 = \(40^\circ\)

### Step 3: Set up the equation
Let the fourth angle be \(x\). According to the property of quadrilaterals, we can write the equation:
\[ 110^\circ + 50^\circ + 40^\circ + x = 360^\circ \]

### Step 4: Calculate the sum of the known angles
First, we add the known angles:
\[ 110^\circ + 50^\circ + 40^\circ = 200^\circ \]

### Step 5: Substitute the sum into the equation
Now, we can substitute the sum of the known angles back into the equation:
\[ 200^\circ + x = 360^\circ \]

### Step 6: Solve for \(x\)
To find \(x\), we subtract \(200^\circ\) from both sides:
\[ x = 360^\circ - 200^\circ \]
\[ x = 160^\circ \]

### Conclusion
The fourth angle of the quadrilateral is \(160^\circ\).