The measure of the four angles of a quadrilateral is in the ratio 3: 5:9:13. The measure of the largest angle is

Options

A. `180^@`
B. `166^@`
C. `156^@`
D. `108^@`

Answer

To find the measure of the largest angle in a quadrilateral where the angles are in the ratio 3:5:9:13, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Ratio**: The angles of the quadrilateral are given in the ratio 3:5:9:13. Let's denote the angles as \(3x\), \(5x\), \(9x\), and \(13x\).

2. **Sum of Angles in a Quadrilateral**: The sum of the interior angles of a quadrilateral is always 360 degrees.

3. **Set Up the Equation**: We can express the sum of the angles in terms of \(x\):
\[ 3x + 5x + 9x + 13x = 360 \]

4. **Combine Like Terms**: Combine the terms on the left side:
\[ (3 + 5 + 9 + 13)x = 360 \]
\[ 30x = 360 \]

5. **Solve for \(x\)**: To find the value of \(x\), divide both sides of the equation by 30:
\[ x = \frac{360}{30} = 12 \]

6. **Find the Largest Angle**: The largest angle corresponds to the largest ratio, which is \(13x\):
\[ \text{Largest Angle} = 13x = 13 \times 12 = 156 \text{ degrees} \]

### Conclusion:
The measure of the largest angle in the quadrilateral is **156 degrees**.