The angles of a quadrilateral are in the ratio `3:4:5:6`. The respective angles of the quadrilateral are

Options

A. `60^(@), 80^(@), 100^(@), 120^(@)`
B. `120^(@), 100^(@), 80^(@), 60^(@)`
C. `120^(@), 60^(@), 80^(@), 100^(@)`
D. `80^(@), 120^(@), 100^(@), 60^(@)`

Answer

To find the respective angles of a quadrilateral given in the ratio of 3:4:5:6, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Ratio**: The angles of the quadrilateral are given in the ratio 3:4:5:6. This means we can express the angles in terms of a variable \( x \). Let the angles be:
- First angle = \( 3x \)
- Second angle = \( 4x \)
- Third angle = \( 5x \)
- Fourth angle = \( 6x \)

2. **Use the Sum of Angles in a Quadrilateral**: The sum of the angles in any quadrilateral is always \( 360^\circ \). Therefore, we can write the equation:
\[ 3x + 4x + 5x + 6x = 360^\circ \]

3. **Combine Like Terms**: Combine the terms on the left side of the equation:
\[ (3 + 4 + 5 + 6)x = 360^\circ \]
\[ 18x = 360^\circ \]

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

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

6. **List the Angles**: The respective angles of the quadrilateral are:
- \( 60^\circ, 80^\circ, 100^\circ, 120^\circ \)

### Final Answer:
The respective angles of the quadrilateral are \( 60^\circ, 80^\circ, 100^\circ, \) and \( 120^\circ \).