The angles of a quadrilateral are in the ratio `3:4:5:6`. The largest of these angles is

Options

A. `45^(@)`
B. `60^(@)`
C. `36^(@)`
D. `48^(@)`

Answer

To find the largest angle of a quadrilateral whose angles are in the ratio 3:4:5:6, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Ratio**: The angles of the quadrilateral are given in the ratio 3:4:5:6. This means we can represent the angles as:
- First angle = 3x
- Second angle = 4x
- Third angle = 5x
- Fourth angle = 6x

2. **Sum of Angles in a Quadrilateral**: The sum of the interior angles of a quadrilateral is always 360 degrees. Therefore, we can write the equation:
\[ 3x + 4x + 5x + 6x = 360 \]

3. **Combine Like Terms**: Combine the terms on the left side of the equation:
\[ 18x = 360 \]

4. **Solve for x**: To find the value of x, divide both sides of the equation by 18:
\[ x = \frac{360}{18} = 20 \]

5. **Calculate Each Angle**: Now that we have the value of x, we can find each angle:
- First angle = \(3x = 3 \times 20 = 60\) degrees
- Second angle = \(4x = 4 \times 20 = 80\) degrees
- Third angle = \(5x = 5 \times 20 = 100\) degrees
- Fourth angle = \(6x = 6 \times 20 = 120\) degrees

6. **Identify the Largest Angle**: Among the calculated angles (60, 80, 100, and 120 degrees), the largest angle is:
\[ 120 \text{ degrees} \]

### Final Answer:
The largest angle of the quadrilateral is **120 degrees**.