If the angles of quadrilateral are in ratio of 1:2:4:5 then largest angle is

Options

A. `75^(@)`
B. `150^(@)`
C. `100^(@)`
D. `80^(@)`

Answer

To find the largest angle of a quadrilateral where the angles are in the ratio of 1:2:4:5, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Ratios**:
The angles of the quadrilateral are given in the ratio 1:2:4:5. Let's denote the angles as:
- Angle A = 1x
- Angle B = 2x
- Angle C = 4x
- Angle D = 5x

2. **Using the Sum of Angles in a Quadrilateral**:
The sum of the angles in a quadrilateral is always 360 degrees. Therefore, we can set up the equation:
\[ A + B + C + D = 360^\circ \]
Substituting the expressions for the angles, we get:
\[ 1x + 2x + 4x + 5x = 360^\circ \]

3. **Combining Like Terms**:
Combine the terms on the left side:
\[ (1 + 2 + 4 + 5)x = 360^\circ \]
This simplifies to:
\[ 12x = 360^\circ \]

4. **Solving for x**:
To find the value of x, divide both sides of the equation by 12:
\[ x = \frac{360^\circ}{12} = 30^\circ \]

5. **Finding Each Angle**:
Now that we have the value of x, we can find each angle:
- Angle A = 1x = 1(30) = 30 degrees
- Angle B = 2x = 2(30) = 60 degrees
- Angle C = 4x = 4(30) = 120 degrees
- Angle D = 5x = 5(30) = 150 degrees

6. **Identifying the Largest Angle**:
Among the angles calculated, the largest angle is:
\[ \text{Angle D} = 150^\circ \]

### Final Answer:
The largest angle in the quadrilateral is **150 degrees**.

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