The adjacent angles of the rhombus are in the ratio of 4 : 5. Find the difference between the larger and smaller angle.

Options

A. `10^@`
B. `20^@`
C. `15^@`
D. `25^@`

Answer

To solve the problem, we need to find the difference between the larger and smaller angles of a rhombus, given that the adjacent angles are in the ratio of 4:5.

### Step-by-Step Solution:

1. **Understand the properties of a rhombus**:
- A rhombus has two pairs of adjacent angles that are supplementary, meaning they add up to 180 degrees.

2. **Set up the ratio**:
- Let the smaller angle be represented as \(4x\) and the larger angle as \(5x\), based on the given ratio of 4:5.

3. **Write the equation for the sum of the angles**:
- Since the adjacent angles are supplementary, we can write the equation:
\[ 4x + 5x = 180 \]

4. **Combine like terms**:
- Simplifying the left side gives:
\[ 9x = 180 \]

5. **Solve for \(x\)**:
- Divide both sides by 9:
\[ x = \frac{180}{9} = 20 \]

6. **Find the angles**:
- Now substitute \(x\) back into the expressions for the angles:
- Smaller angle: \(4x = 4 \times 20 = 80\) degrees
- Larger angle: \(5x = 5 \times 20 = 100\) degrees

7. **Calculate the difference**:
- The difference between the larger angle and the smaller angle is:
\[ 100 - 80 = 20 \text{ degrees} \]

### Final Answer:
The difference between the larger and smaller angle is **20 degrees**.