The angles of quadrilateral are in the ratio `1:3:7:9` The measure of the largest angle is

Options

A. `63^@`
B. `72^@`
C. `81^@`
D. None of these

Answer

To find the measure of the largest angle in a quadrilateral where the angles are in the ratio 1:3:7:9, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Angles**:
Let the angles of the quadrilateral be represented as:
- First angle = \( x \)
- Second angle = \( 3x \)
- Third angle = \( 7x \)
- Fourth angle = \( 9x \)

2. **Use the Property of Quadrilaterals**:
The sum of the angles in a quadrilateral is always \( 360^\circ \). Therefore, we can write the equation:
\[ x + 3x + 7x + 9x = 360^\circ \]

3. **Combine Like Terms**:
Combine the terms on the left side:
\[ (1 + 3 + 7 + 9)x = 360^\circ \]
This simplifies to:
\[ 20x = 360^\circ \]

4. **Solve for \( x \)**:
To find \( x \), divide both sides by 20:
\[ x = \frac{360}{20} = 18^\circ \]

5. **Calculate Each Angle**:
Now that we have \( x \), we can find each angle:
- First angle = \( x = 18^\circ \)
- Second angle = \( 3x = 3 \times 18 = 54^\circ \)
- Third angle = \( 7x = 7 \times 18 = 126^\circ \)
- Fourth angle = \( 9x = 9 \times 18 = 162^\circ \)

6. **Identify the Largest Angle**:
Among the calculated angles, the largest angle is:
\[ 162^\circ \]

### Final Answer:
The measure of the largest angle is \( 162^\circ \).

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