If the angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4 . Then, the measure of angles in descending order are

Options

A. `36^(@), 108^(@), 72^(@), 144^(@)`
B. `144^(@), 108^(@), 72^(@), 36^(@)`
C. `36^(@), 72^(@), 108^(@), 144^(@)`
D. None of these

Answer

To solve the problem of finding the angles of a quadrilateral in the ratio 1:2:3:4, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Ratio**: The angles of the quadrilateral are given in the ratio 1:2:3:4. Let's denote the angles as follows:
- First angle = \( x \)
- Second angle = \( 2x \)
- Third angle = \( 3x \)
- Fourth angle = \( 4x \)

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

3. **Combine Like Terms**: Simplifying the left side of the equation:
\[ 10x = 360 \]

4. **Solve for \( x \)**: To find the value of \( x \), divide both sides by 10:
\[ x = \frac{360}{10} = 36 \]

5. **Calculate Each Angle**:
- First angle: \( x = 36^\circ \)
- Second angle: \( 2x = 2 \times 36 = 72^\circ \)
- Third angle: \( 3x = 3 \times 36 = 108^\circ \)
- Fourth angle: \( 4x = 4 \times 36 = 144^\circ \)

6. **List the Angles**: The angles of the quadrilateral are:
- \( 36^\circ, 72^\circ, 108^\circ, 144^\circ \)

7. **Arrange in Descending Order**: To write the angles in descending order:
- \( 144^\circ, 108^\circ, 72^\circ, 36^\circ \)

### Final Answer:
The measures of the angles in descending order are:
- \( 144^\circ, 108^\circ, 72^\circ, 36^\circ \)

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