The angles of a quadrilateral are in the ratio 5:3:9:7. Find the angles.

Answer

To find the angles of a quadrilateral that are in the ratio 5:3:9:7, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Angles in Terms of a Variable:**
Let the angles of the quadrilateral be represented as:
- First angle = \(5x\)
- Second angle = \(3x\)
- Third angle = \(9x\)
- Fourth angle = \(7x\)

2. **Set Up the Equation for the Sum of Angles:**
We know that the sum of the angles in a quadrilateral is always \(360^\circ\). Therefore, we can write the equation:
\[ 5x + 3x + 9x + 7x = 360 \]

3. **Combine Like Terms:**
Now, let's combine the terms on the left side:
\[ (5 + 3 + 9 + 7)x = 360 \]
Simplifying this gives:
\[ 24x = 360 \]

4. **Solve for \(x\):**
To find \(x\), divide both sides of the equation by \(24\):
\[ x = \frac{360}{24} \]
Simplifying this gives:
\[ x = 15 \]

5. **Calculate Each Angle:**
Now that we have the value of \(x\), we can find each angle:
- First angle: \(5x = 5 \times 15 = 75^\circ\)
- Second angle: \(3x = 3 \times 15 = 45^\circ\)
- Third angle: \(9x = 9 \times 15 = 135^\circ\)
- Fourth angle: \(7x = 7 \times 15 = 105^\circ\)

6. **List the Angles:**
Therefore, the angles of the quadrilateral are:
- \(75^\circ\)
- \(45^\circ\)
- \(135^\circ\)
- \(105^\circ\)

### Final Answer:
The angles of the quadrilateral are \(75^\circ\), \(45^\circ\), \(135^\circ\), and \(105^\circ\).