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

Options

A. `90^(@)`
B. `120^(@)`
C. `150^(@)`
D. `102^(@)`

Answer

To solve the problem of finding the largest angle in a quadrilateral where the angles are in the ratio 3:4:5:6, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the sum of angles in a quadrilateral**:
The sum of the interior angles of a quadrilateral is always 360 degrees.

2. **Set up the ratio**:
Let the angles be represented as:
- First angle = 3x
- Second angle = 4x
- Third angle = 5x
- Fourth angle = 6x

3. **Write the equation for the sum of angles**:
According to the property of quadrilaterals, we can write the equation:
\[ 3x + 4x + 5x + 6x = 360 \]

4. **Combine like terms**:
Combine the terms on the left side:
\[ (3 + 4 + 5 + 6)x = 360 \]
This simplifies to:
\[ 18x = 360 \]

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

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

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

### Conclusion:
Thus, the largest angle in the quadrilateral is **120 degrees**.